Call it in, because this sounds like a hardware issue with your new system.
If you want to get a jump on things, while you're waiting on hold, you can run Apple Hardware Test. Load the OS X install DVD into the drive and reboot holding down the "D" key. Odds are they're going to ask you to do this anyway, so may as well get started now.
It's entirely possible that will pinpoint a specific problem with the system (I'd suspect an issue with the logic board) and then you can set up a repair at a nearby Apple Store or AASP. The alternative to that is mailing the system to an Apple repair facility, and that will probably take a minimum of a week.
One other thing you can try, is wiping the drive clean, installing a fresh copy of the OS, and then seeing what happens. While unlikely, it's possible there's an issue with one of the apps you brought over from the old system. It's one more thing to rule out if nothing else.
after transferring successfully all apps, etc. from my MacBook which runs 10.5.6 to a new MacBook Pro running 10.6.3 everything is fine EXCEPT:
1. when downloading large map file from Garmin website to my GPS's MicroSD card running Safari, which took forever, I came back to computer after awhile and there was the login screen - either MacBook Pro did a Restart or a Log Out - this happened repeatedly & I gave up on the download - I never saw it actually happen as I just couldn't watch the computer every second for the hour or so this download went on.
2. Exact same thing happened (either a Restart or Log Out all by itself) when I was backing up to a Firewire external drive using SuperDuper, no other apps open - the first time the backup did not complete according to SuperDuper log after I logged back into MacBook Pro; the second time, the backup was successful according to the SuperDuper Log, but still, when I came back to computer after walking away during the backup, there was the Login screen.
3. Same thing happened when I did a Time Machine backup the first time! The second backup attempt with Time Machine did work as far as I can tell (although the log info, etc. with Time Machine doesn't seem to exist, doesn't say "backup successful" or anything) and also this second time backing ujp with Time Machine DID NOT trigger the restart or log in thing.
I had several times in past done a similar download from Garmin, and many, many times backed up to external Firewire drive using SuperDuper on my older MacBook running 10.5.x and NEVER saw anything like this happen. Again, nothing changed between my MacBook 10.5.x and my MacBook Pro 10.6.3 other than system -- all the apps are the same - this is a brand new machine and I just used Migration Assistant to copy over, etc.
I thought Norton Antivirus might have been the problem, but with all protections turned off, the 10.6.3 MacBook Pro STILL either restarted itself or logged out (I can't tell which - I just know that when I returned to machine I had to log back in, etc.) I also tried turning off screensaver and all Sleep options, including hard drive but this didn't help.