Your computer will write all data that is in memory to the hard drive when it enters hibernation to the hibernation file on your disk and then shut down. That's normal.
To resume operation, one must push the power button on, the system awakes, finds the hibernation file, loads that into memory, and your session starts again where it left off when you initiated hibernation. That is normal too.
The reset button is either for the computer or the monitor. Not clear which you meant. If, the monitor will not enter energy-saving mode when in normal operation (screen goes dark after so many minutes), then issue could be with the monitor itself and/or the video card and not have anything to do with XP going into hibernation and coming back out.
Looks like a possible hardware issue from here. Try another monitor to see if you get the same behavior.
Windows XP When computer goes into hibernation monitor switches off and won't come back on until you use reset button