My friend got an "as-is" $80 Xbox 360 without a warranty sticker or a controller, A/V cords, or a power cord off of eBay awhile back (I know

). It worked just fine for awhile. I modded the firmware on its DVD-ROM drive for him a few weeks ago, just before Halo 3 came out. It was working fine, but then it got the RRoD. Via pressing sync and eject, we figured out the problem to be the GPU overheating. So, we opened it back up, cleaned off the old thermal gel, and replaced it with new thermal gel, put it back together, and we still got the RRoD.
A few questions:
Where should I go from here in my neverending quest to fix the RRoD?
Could my modding of the firmware have influenced the RRoD?
Is it possible to just replace the motherboard, still using the original disc drive/other stuff?
Thanks.