Does anything work  

My Microsoft Office 2000 is on disc and I have the 25-character product key.
Since I can use Microsoft Office 2000 on either my 32-bit or 64-but Win 10 OS’s I don’t see why you can’t use Office 2003. I was using Microsoft Office 2000 until Feb 2017. That’s when I went with Microsoft Home and Student 2016. The main reason is because where I volunteer, we interact with local and state agencies and it was time for me to get up to date: but on top of that we have about 200 volunteers and some of them are involved with our data & documents, but when it comes to deal with the differences between Microsoft Office programs along with the freebies, the issues are even though the documents and data can be read, the ability to edit and correct items are not possible especially to ensure consistency on how they are managed for our data management. As far as cost, I believe the cost for my Microsoft Office 2000 was about $120.00 back then then: the average cost per year until 2017 is minimal. On my Microsoft Office Home & Student 2016, it cost me a total of about $150.00 and I expect to continue using it for “umpteen” years and the average cost per year to be minimal.

Anyway, if you can’t install your Office 2003 on whatever Windows 10 version you have, it does sound like you need to an in-place upgrade as has been mentioned by Clintlgm’s advice in post #19 is a very good.
If the in-place-upgrade doesn’t work a clean install might be called for.

Unless I missed it, we don’t know if you have an Office 2003 disc or are relying on the 25-character product key.
The idea is if you can get whatever Windows 10 version you have to run properly, you could try to install your Office 2003 again but know that Microsoft will not help on a program that has reached end-of-life: error code 1935 or anything else.

You don't indicate what version of W10 you are using. If it's 1803, you may be experiencing the same issue many others had when 1803 was first released. I don't remember all of the details, but Excel would not work at all. In my wife's case Office 2003 was already installed when her system automatically upgraded to 1803, so just run errors, not update errors. Since it wouldn't run properly, maybe your install problems are related. Now, many updates later, Office 2003 seems to work on Windows version 1803. Maybe you are missing some updates?

Clintkgn thanks for that info. It just seems a lot of work for something that should not be failing to begin with.. I am about 95% sure I am going to reinstall Windows again. I have little or NO faith that will fix any of the problems I have encountered with Windows 10.

MeAndMyComputer - yes I do have the original Office 2003 install disc. I was also told before trying to install any of the free Office programs I needed to makes earlier attempts had be removed from my PC.. I would have to check on how to do that, but I believe I did that already before the last attempt to install any Office.

Have a great day

@ Huffman re post #23

"Clintkgn thanks for that info. It just seems a lot of work for something that should not be failing to begin with.. I am about 95% sure I am going to reinstall Windows again. I have little or NO faith that will fix any of the problems I have encountered with Windows 10."
--- I agree with Clintkgn input: if the computer needs a clean start, that needs to be done or a re-install as you mention.
--- Personally I prefer a clean install in your case.
--- I know what you mean by having "NO faith"
--- Create a system restore point, a system image backup onto an external HDD and save your data separately also.
--- When you are ready please create a thread on how to accomplish whatever "clean-up" of your OS needs so we can help you get off to a good start and a successful solution.
--- Trying to solve a legacy product such as Office 2013 on a troubled computer can be counter-productive.

"MeAndMyComputer - yes I do have the original Office 2003 install disc. I was also told before trying to install any of the free Office programs I needed to makes earlier attempts had be removed from my PC.. I would have to check on how to do that, but I believe I did that already before the last attempt to install any Office."
--- That's sounds good but I don't understand what you mean by "free Office programs" relative to Office 2013.
--- How is Office 2013 a "free Office" program?

Last but not least, if you haven't tried it yet run sfc /scannow. Let us know the results.

MeAndMyComputer . yes I did run sfc /scannow. It came back and said everything was good. LOL I know that is BS.

Huffman please we cannot see your computer and I am not aware you have run sfc /scannow.
If I missed it let's move on anyway. It is not BS but it is a beginning to logical troubleshooting.

Post #1 "I have only had Windows 10 for just over a week"
--- What was your prior OS? Can you get back to it?
--- How did you get from Windows 7 to Windows 10?
--- Was the computer running ok when it was on Windows 7?
--- What make/model is your computer?

On the error 1935, I haven't found anything that addresses it in Office 2003.
Post #5 "Also so I have tried installing the free office softwares and I get the same 1935 Error"

Post #18: "I have probably got that PC so screwed up by now, it is a wonder anything works."
--- That's a very important statement but we don't know what all of that means.
--- Is it better to troubleshoot the computer or conduct a Repair Install Windows 10 with an In-place Upgrade as has been mentioned?
--- Try the Repair Install Windows 10 with an In-place Upgrade.

If you have data to save, save it.

Like I have said before: It seems like every time I try to do almost anything Windows 10 balks. Here I am mainly speaking about installing software. Here is an example"

I have Macrium Reflect installed and about a week ago I created an image (or at least I thought I did). This morning 10 was acting so erratic I decided I want to put that image back. LO and BEHOLD. Macrium does not recognize the image I made (it is stored on an external HD). In Files I do see the image file.

That is just a crazy example.

That's a pretty good example. What make/model computer do you have?
Please fill in your computer specs.
System Specs - Fill in at Ten Forums | Tutorials

Save your data manually: copy/paste onto your external HDD and/or a USB flash drive.

I would consider a clean boot
Perform a Clean Boot in Windows 10 to Troubleshoot Software Conflicts | Tutorials
--- If it takes a while, stay with it.

MeAndMyComputer I am going to take another look at how to use Macrium Reflect. I could have and probably did make a mistake.

TairikuOkami - Just how do I upgrade without having to pay again. Here is example of what have seen at Microsoft. I talked to a technician at Microsoft about a week ago and wanted to change my password for my Microsoft accounts. They were glad to do that for me for only a fee of $80. I told him in no uncertain terms what he could do with his tech service.

huffman said:

MeAndMyComputer I am going to take another look at how to use Macrium Reflect. I could have and probably did make a mistake.

Excellent. Check for MR updates before you begin. Also create up-to-date rescue media.
Upon completion check that the rescue media will boot up and be able to restore the system image backup.
I've been using Macrium Reflect Free for years w/o any problems.
I do mine manually at the end of each month so my computer will be ready for the upcoming month's WU's.
--- Also when I want to conduct experiments.