looking for a couple used 500/2000 2.04 Roms

[Oldsmobile_Mike]

You mean Tekmagic?

When did you send it to GVP?  Recently?  Afaik they haven't been servicing boards in over a decade...

In any case, you shouldn't have any problem using it with a 6.x-series motherboard and the latest 3.1 ROM.  Using an '060 under 2.04/2.1 would be like using a Formula 1 race car on "Ron's Discount Retread Tires".  Don't do it, it *will* work under 3.1.  How do I know?  Because I own one, lol.  

If you suspect ROM issues, try with a new 3.1 chip first.  You can get a new one for under $20 USD:

http://amigakit.leamancomputing.com/catalog/product_info.php?cPath=25&products_id=157

I'd try that, and start documenting everything you've tried.  I.e., does the A2000 boot normally with no accelerator installed, what exactly happens when you try to boot with the board installed, any battery damage, reseated all the custom chips (on the Amiga and on the GVP board), also it might be an issue of your PSU starting to fail and not putting out enough power.  Have you tested that?

This page has some additional info that may help you:  http://nishtek.com/Riese/GVPTekmagic68060.html

[Oldsmobile_Mike]

When I installed my Tekmagic '060 I already had a GVP '040 board installed and running with the '040 version of THoR's libs.  I swapped the boards and powered it on, it threw a flashing yellow error message something about needing the right '060 libs, or the dummy '040 lib (I forget what it said, exactly), but once I installed the '060 versions of the libs, datatypes, and '060-specific versions of the other utilities I run, all was back to normal.

TL;DR.  THoR's libraries should work fine for you.

Maybe I missed it, but to be specific - are you saying when you try to use the board your system doesn't power up at all (a hardware problem) or tries to power up, but gives errors (a software problem)?

Are you able to test the system with another board in the CPU slot?  Check continuity on the pins on the MB connector?