No Chime, No boot up - just fan noise on my Mac Pro 3,1

The chime on a Mac (of that era) is an indication that the core hardware is working correctly. No chime means that there is some hardware problem.

If it was simply a question of no bootable drive, then you would get the chime, followed by a flashing question mark on the screen.

I would re-open it and make sure that you have correctly re-seated the RAM and other components, after your strip-down. If you unplugged any internal cables, make sure they are all re-connected.

You might want to follow an iFixit guide for stripping down your model of Mac, which may also provide notes about common re-assembly problems.