That system is an early 2008 system. Its long past Dells warranty period so there will likely be no more driver updates. It should work on a Clean Install of Windows 10 however, see here for details:

http://dellwindowsreinstallationguide.com/a-clean-install-of-windows-10/

I've had the same problem.   I upgraded an older i630 to Windows 10 Pro and it has been a nightmare.   The computer would either lock up tight or restart without  warning.   Sometimes it would restart 2 minutes after bootup, other times 25 minutes in.   I assumed the power supply was failing and I ordered a new OEM Dell Power supply from eBay and installed it.   Replacing it was a nightmare because the motherboard power cables ran underneath the motherboard requiring removing the entire motherboard just to replace the power supply.   But all of that effort was in vain because the computer continued to crash and restart even with a brand new power supply installed.  I assumed it would work fine because I didn't have a problem at all with my AIO 27 Touch 2710 Dell or my Inspiron 17R laptop.   Both those computers upgraded fine to Windows 10 Pro.

To add insult to injuring, now I'm getting a CPU Fan failure error message at bootup since I had to remove the heatsink to remove the motherboard.  Not sure what's wrong yet because I can physically see all the fans spin up.  I added fresh thermal paste between the CPU and the heat sink and connected the power connector from the heat sink back into the motherboard plug again.  

I learnt a lesson, next time I will not be in a rush to upgrade an older PC to the latest Windows.   And I will google around for anyone else having problems before I undertake another upgrade like this again.  It's unfortunate, the i630 was a good computer despite the *** original nvidia 8800GT cards it came with.   SLI never did work well on the 630.     

These do work fine with Win10 - as long as you switch off the Nvidia Raid - and just use ata mode on the drives

Dell or any PC for that matter make good paperweights when Microsoft come's out with a new OS, I have a XPS 630i, that runs as good as it did the day I bought it, but slowly all the browsers are acting up and not supported. This is my third Dell, I have thousands invested in software for PC's,  no longer supported, the reason I stayed with Dell/PC, Now I'm looking at Ten Reasons Macs Are Better Than PCs, saying good bye to PC's, I've had enough.

I also have the 2008 XPS 630 and am also having some of the same issues. Initially after I installed W10 the Internet would stop working after a while, and the only fix was restarting the computer after which the internet would shut off again. I managed to fix it with a command in the command prompt.

My video game FPS also went way down after I installed the W10 free upgrade.