Wolfman86, looking at your dumps it seems quite strange, so:
- 062710-24554-01.dmp, system (win7 x86) crashed (memory fault), but avast wasn't even installed; have you tested both computers with memtest86+? since it seems like a hw problem here (are all your memories modules running on the same frequency, etc?)
- 062710-20186-01.dmp, system (win7 x64) crashed in our driver (memory fault), but that chunk of memory, it was tried to read, was valid - although the system crashed...
btw, win32k.sys crashes are quite rare and they're not usually caused by applications/other drivers...