Both computers with the same hardware, only difference is 2 GB of ram in 32-bit installation and 4 GB of ram in 64-bit installation. Same version of java and everything, it crashed before game even ran in 1.6.4 and around 5 seconds after loading the map in earlier versions.
This happens only on x64 computers with 64-bit Windows(no matter if java is 64 or 32-bit). I've tested it. x64 with 32-bit OS works fine.
My GPU is legacy(Radeon X1950 Pro), version of driver(not catalyst) 2010.0210.2339.42455.