Still not allowing Internet acces, claims it's the router.

Hardware. HP DV6000 RX945AV laptop, or as SIV identifies it, a Compaq Presario V6133CL (it also shows the DV6000 RX945AV). HP site has Vista drivers for the Compaq, only XP for the HP, despite the fact Vista was an available option. (They're the same bleeping laptop, despite minor cosmetic diffs!)
AMD Turion 64 X2 CPU.

Ethernet adapter is nVidia nForce
WiFi is Broadcom 802.11g

Windows 10 build 1511 with the July 12 Servicing Stack Update.

The symptom is the same one so many have suffered with. "Connected" by LAN or WiFi but "limited". Run the troubleshooter and it flat out lies to the user that the problem is the router or modem isn't communicating with the internet, while other computers are having no problem. It may also pull the other one and claim "Problem? No problem here!"

I can get it to work by running an elevated Command Prompt, doing NETCFG -D twice, closing the command prompt then rebooting.

That works until it's rebooted or shut down then booted up again.

What makes this problem especially annoying is it doesn't pop up right away. The internet connection worked long enough for the 10 upgrade to download updates (for some reason it missed the Servicing Stack Update, I had to install that offline) and for some hours after it was finished then suddenly *PLIP* no internet and it's been resisting getting fixed ever since.

I have installed a slightly modded version of the latest BIOS which removed the whitelist for mini PCIe WiFi adapters, so I could install a different one to try. I have several but they're all from the Windows Vista to 7 era so would likely experience the same problem. Swapping out the WiFi wouldn't do anything for the built in Ethernet.

Does anyone have any nForce and Broadcom drivers that have stayed working?

it looks like your laptop is older than 7 years as HP does not support that one anymore, has not even drivers listed. Nevertheless it should not be too old to run Windows 10. If it installs, it runs. I myself have a HP Compaq NX9420 that runs Windows 10 just fine.
I think your case is a driver issue. With old hardware one has to get a little creative. Getting the right driver for Windows 10 is sometimes a little tricky. I myself usually look at the HardwareID and begin looking for drivers that way. Has worked for me so far. Just look at the HardwareID of your LAN and Wifi components, copy and paste and let google (or your preferred search engine) do the rest.

For the Broadcom WiFi I finally found a Windows 7 driver from HP. sp47895.exe Had to extract it with WinRAR. For the Ethernet I searched the WHQL library for nforce network controller and downloaded the newest one for Windows 7. Had to extract the CAB with WinRAR.

To install required digging down through Device Manager to Have Disk. 21 years later and this is exactly the same as Windows 95, still prompts for a floppy disk!

The broadcom WiFi drivers for Win 7 from WHQL are missing the MD5 hash in the catalog file so 10 flat out refuses to accept it, even with driver signing disabled.

Four Windows 10 upgrades and every one I've had this same fight with networking, but once drivers that 10 finds acceptable are forced into it, it appears to work as it should.

Odd thing is, the first one, a MPC TransPort T2500 laptop made in 2008, Just Worked. The only driver I had a problem with was for the Memory Stick function of the Ricoh card reader. But then comes July 2016 and a 16 day trip, not updated to the 1511 build and it would only stay working on WiFi at two of the hotels I stayed at. Prior to that it worked fine on my home WiFi and a few other places I took it to.

The TransPort T2500 is a Core 2 Duo, actually a rebranded Samsung X65. All Micron Computer, MicronPC and MPC laptops from the first in the mid 90's through the bankruptcy of MPC in 2008 were Samsungs. Most of them were very high end computers.

The T2500 was the first one I upgraded to 10. Then I did a Dell Inspiron 530, one of the variants which accepts a quad core CPU and 8 gig RAM. Then I did my main desktop which is a built it myself Socket AM2+ with an AM3 dual core CPU in it. The desktops were not much of a problem with the networking, but the T2500 took more searching to find suitable network drivers.

I put 10 on the DV6000 mainly just to see if it would work, and it does fine since I found Windows 7 drivers for the GPU and network controllers. If it was a GeForce 6150LE it would've been easier because nVidia's driver package directly supports it.

But the common thread among the four was that *initially*, for some period of time, the internet connection worked - then suddenly the problem started. If it works to start with (especially after 10 takes over during later stages of installing and downloading updates), with the drivers Windows 10 installs, why should it suddenly stop working until different drivers are installed? Like I've said before, the T2500 was fine with the RTM release of 10 for nearly a year then this July it acted up.

One of the neatest things about the Samsung (and others selling them under their name) laptops is through that entire period Samsung used the same power specifications and the same power connector on the laptops so the same 19 volt power bricks and 12 volt vehicle adapters will work on all of them. AFAIK, no other computer company has done that.