Main board is fried. The only thing that'll cause it not to POST that isn't soldered to the board is the RAM, and dead or "missing" RAM should cause the system to beep annoyingly before giving up.

That laptop is worth maybe $50 on its best day in perfect condition, so it's probably time to scrap it.

You should still be able to get a few generations newer (6430, 40, etc) for cheap on eBay (though not as cheap as a year ago), and those are still quite usable with an SSD--if your "customer" needs to replace the system on the cheap that's what I'd do.