I have an HP Pavilion xg836 - translated that means a Celeron 733 mhz processor, two memory slots w/512mb total usable, and a FSB speed of 66mhz. For the last five years I have been running it with two 64mb DIMMS without problems except for not a lot of real memory.

Recently was able to afford to upgrade so bought two 256mb DIMMS - AO16C3264 PC133. I popped them in instead of the 64mbs, powered up, bios screen said 512mb memory, Windows 2K PRO starts up then dies with blue screen telling me my system is not completely compatible with ACPI standard.

OK, into troubleshoot mode. Each DIMM singlely works find, lasts long time. One 256, one 64 works fine, lasts long time. Two 256, blue screen of death.

Bios is Phoenix 4.0 Release 6.0 version 2.03. Mobo is Trigem Cognac. Any ideas or suggestions?

This sort of prob. was evident in w98, it's ram threshhold was around 600mb and the BSOD was a common occurance. Anything more and you might actually get to desktop but the OS was unstable.
Such is what I experienced here myself. Only one of two avenues were practical, drop the excess ram or upgrade the OS to the next higher level. Here, it was a bit late in the day for 2K or ME so I went with XP.
It's a driver issue, to which 2K is apparently unsuited.