Cannot "re-boot" when I use the [Menu+Center button] combo to reset?
I have had this iPod for a while. I am willing to accept a position that repair may be untenable.
"Have you had your ipod connected up to an iTunes installation, have you backed your music / video's up recently? if not do so now.
Do not back up the device itself, as the firmware corruption may transfer onto this back up.
The very first thing i would try is a factory defaults reset of the device. If you can plug it into iTunes the option to do this is located when you click the iPod in the devices section.
Restore it to factory defaults and then load your Music / Video's back onto the device by setting it up as a new iPod (instead of restoring from a back up of a previous one).
This may or may not work depending if this issue is software or hardware related.
The issue sounds like a logic board problem if it is a hardware problem."