Have already given advice which should explain your BSOD causes, but will post here again, as can tell you right now, is a 99% chance is a hardware or driver issue!
Three options, all referring to memory-type errors:
Faulty or mis-matched RAM
Corrupted/faulty page-file (virtual memory) - this can can be fixed by manually setting a higher-than-max required page-file size
faulty hardware drivers
NB: the "0×000000D1" error code way the real clue ;) Do a Google search for that error code for further info
Now, given that you are inquiring regarding Vista trial, it sounds like Win7 is the first OS installed on the new machine, so I do think you are being a little too quick to find Win7 the culprit. Most references to this error are found on Vista or XP. What you will find (especially if the issue comes to mismatched or faulty RAM) is your blue-screens will be ten-fold, given that Vista is more memory-hungry. If a driver issue, XP is likely to give you more hell, as finding XP drivers for new hardware becoming more of a challenge.
Now, first thing to do is pull out all bar one stick of RAM and reboot (have heard some had to do fresh install of Windows - either Vista or Vista, by the way - to try this fix, but usually fine). If working fine, you have the source of your issue.
Also, do you have the latest Win7 specific drivers for your vid-card?? The fact that AMD have release Win7 drivers for GPU already, tells me there is an incompatibility with Vista drivers... otherwise they would have waited till Win7 was actually in full release.
Now you keep making reference to having the "latest" or "highest" ati/amd products. That still doesn't prevent a hardware fault, and is certainly NO guarantee against sh1tty driver encoding... and a cr@appy driver can render even the most advanced hardware inoperable!
From another Win7 x64 user, have rolled out on two notebooks, having hunted down all the drivers I need - latest builds, kept as much of the usual OEM crap-ware off by machines.... runs sweeter than either XP or Vista ever did. Wireless out of the box in both cases, plays every media format I've thrown at it - no codecs required - my hardware (including a 7yo CanoScan scanner working flawlessly) actually handles better than the last two versions of Windows. Not perfect (still annoyed over advanced tag editor being removed from WMP12, and miss the advanced file search options... although found freeware tool that takes care of that), but definitely ten steps up from Vista.