|Is the current laptop the same identical model as the old one was?|
The advice by both helpers above is good. Especially testing the RAM. RAM contacts can get corroded, causing poor conduction. Snapping each RAM module in ad out 4 or 5 times will burnish the contacts. Blowing out the venting is also important. If the CPU fan is seized up that could cause problems if the laptop was calling for it to run.
Those three items are the most likely HARDWARE reasons for the laptop to not boot into windows.
If there are flash drives, memory cards, PC cards or other external hardware connected when booting those devices have the potential to cause issues with windows.
When you transferred the hard drive did you re-install or repair Windows at that time?