Unless something else is wrong,  yes, the system will work on AC only (no battery).

Thanks for the response.  Do you have any suggestions on what to do next?

If what you're saying is the system won't power up, verify that the adapter is OK (LED ON before you plug in the notebook end).  If it's not, replace the adapter.  If it is, try reseating (remove and reinstall) the memory.  If that doesn't work, replace the mainboard.

It's not a trivial task - and the board will be expensive - $350-400 for the part.

No luck with the easy solutions.  How difficult is it to replace the mainboard?  

Thanks for your help.  Sounds like I'm SOL.