Aspire 5610 problems with motherboard

Very simply can be some loose hardware.

First thing is to take the battery out and unplug it from the wall. Plug it back in w/o the battery and try turning it on. If it boots great, if not unplug it to shut it off immediately and try turning it on again. Lot of no boot issues are because the system is in a failed sleep/hibernate and just wont get out of it until you do the above.

Try re-seating the RAM (hopefully it's not under the keyboard or somewhere hard to get). The RAM they ship with these units is low yield stuff so even though the RAM is good, and the slot is good, they're not making a good connection cause it's cheap stuff so you may want to try a different RAM chip all together.

Sometimes it can be a loose processor which is usually a lot harder to get to unless your savvy.