A big mistake help

Short answer - no. If you were to pay some horrendous amount you might get something back, assuming it's a hard drive.

Good thing you have a backup disk - if that's what it is..?

This is also one reason we continually advocate disk imaging - relatively girlfriend-proof provided you keep the backup secure!

By the way I made a Mac... boot disk. If I would have run that would it have erased all my partitions?

If you booted the computer with the Mac OSX disc, and tried to install it, it would have wiped all of your partitions and formatted the Drive for a Mac OS.
As far as recovering, since the new Operating System was installed, it over wrote all of your previous data.
You can try recovery software like the free TestDisk program, but I would assume you will not find anything.
Remember to always have a current backup of your files on more then one drive or Cloud service.

Doing a Quick Format or deleting partitions does not totally remove the data, and the files could have been recovered. However, once you reinstall the OS, it overwrites the data and those files can no longer be recovered.
In the future, if you computer won't boot, you can use a Windows or Linux boot disc to boot the computer and copy the files off of it to an external USB HDD before sending the computer in for warranty repair. Dell probably put in a different HDD in the computer anyways, so there is no data of yours left to recover.

Thanks Every one for replying,

The usb I made I got off of this forum..
MediaCreateTool64.exe

The name is ESB-USB.

It contains folders:
boot
efi
sources
support
It contains 3.25 GBs..
I think its boot only.
I made it before the crash.
I don't think it will work because they formatted everything.

I have an old computer that has the files in it but old.

I know, I know, I should have made a back usb for the files.

I had one but I messed it up just before the crash.

Don Cole