I would have to guess it is not a Windows 7 problem, unless something running is conflicting an causing a problem. Perhaps the ACPI system is not behaving and causing power problems.
Does it make a difference if you have it plugged in (with and without the battery) or not.
Have you loaded any software yourself? Does it do the same thing in Safe Mode.
If you were to run another OS from a DVD, line Ubuntu Linux, do you know if the system shuts down.
You might want to try resetting the Bios to its default values to see if it helps. You may want to make note of the current settings in case you want to go back.
When they replaced the Motherboard, did they swap over the memory and all other components or give you new?