Take the battery out and try to power on using only the power supply.
If you have the same problem, a faulty battery isn't to blame and your power jack + power supply should be okay.
The next best bet is the memory. Try taking it out and reseating it. Even better, if you have two modules of memory, try each one by itself.
Aside from that, there's not a lot you can do other than try to reseat and remove components. And on a laptop, most of those are on the inside... and it is quite a #$%^ to get most of them apart. You're best off contacting the manufacturer and getting it fixed under warranty, or by a local computer shop that deals with computer repair (component level).