In basic agreement with C_jack. Unless you've some ability to comprehend a wiring schematic of the unit, you're basically shooting in the dark with a blindfold on attempting a do-it-yourself. The...

>>>main power
You mean the AC adapter?

It's been out for a while and a possible cheap way out is another rechargeable batt.

Another thought, have you tried a different GA?

GA = Graphics Adapter (video card)

you've apparently found your prob., i.e. bad cable. until repaired/replaced the fix you've found may not hold too long.
yep, you could at least try the...

When booting up the GA uses basic settings, however, when the OS takes hold IT'S using enhanced mode drivers. Try booting in Safe mode for a check.
The drivers may be corrupt and may need to be...

This is hardware issue. Given the age of the machine I'd check for a contaminated set of cooling fins. Short of that I'd take the card back to the retailer for a refund/replacement.