It sounds like a fixable intermittent circuit board problem to me. A GPS is a computer, so if the power cuts out even briefly, it will then reboot, which may make the problem look worse than it is.
Be careful about static electricity on top of what sounds like a CRT monitor!
It sounds to me like your unit is still fixable, but be aware that *static electricity* can - in a second, permanently destroy the CPU, making the unit *much* more difficult to fix.
If you open the case up, you'd be smart to do a little reading on ESD first. Its quite easy to minimize ESD. You just need to keep yourself and any tools you use grounded. (Typically people use a wire connected to a grounded plug - connected via a strap attached to a wrist or similar)
Its still early in the year and the humidity is still low enough to make ESD a big potential problem. When or where the humidity is higher, ESD is a non-issue.
Check out the instructables site and sparkfun.com for lots of good basic info on electronics.