All battery's get hot when used moderate or hard, no matter if they are new or old, but when they are old and capacity is down they have to "work" harder because the discharge rate (C) will be higher due to the lower capacity:
1320mAh drained at 500mA = 0.38C ("normal" work)
1100mAh drained at 500mA = 0.45C ("harder" work)

on the problem:
Sounds like there is a problem with your N900, one last thing is to take the battery out, press power button without battery or usb, see if this helps, if not try again and also short the + & - terminals in the phone (again without battery or usb), now try to turn on the n900 with the battery.