For most 32 bit is fine but the industry has been pushing 64bit heavy for the last few years (for really no good reason for most users). Tests have been done on the same computers comparing 32bit and 64bit and only a few applications (Photo/Video editing, etc.) are significantly faster with 64bit.
I would bet it's the 64bit version that is the problem.I have nine computers and eight of the nine I've successfully upgraded to Windows 10 32-bit (Some Home and some Pro).I stayed in the 32 bit world and am happy I did.I have no reason to go more than 32bit as 4gb RAM (3.2 to 3.5 depending on the system) is just fine for what I do.I'm not a gamer so I don't need a super uber video card (All my video cards are 512MB ram).And most applications are still 32bit only.
RUNNING PCAD 2006 ON WINDOWS 10 64BIT DRIVERS
Sorry I couldn't give you a more definitive answer but at this point the decision on which systems will receive Win10 drivers hasn't been finalized. It has a ton of good information on Win10 and what you can expect to see regarding that OS, drivers, etc.
You may want to check this great FAQ post about Windows 10 that one of our community members created. NVIDIA themselves may release drivers for it and I recommend you check their site when we get closer to the Win10 launch, as well as our support site, to see if drivers are indeed released. That being said, the D620 was a great system (I had one for years) but considering the age of that system, they premiered in 2006, it's highly doubtful in my opinion, that Dell will provide new drivers for those NVIDIA cards. Until they are, and that won't happen until closer to the release date, we can't definitively say which systems will and will not have drivers released by Dell that are Win10 compatible. The final specs and requirements for Windows 10 have not yet officially been released.