Sounds to me like possibly the AC charging adapter is bad and the battery is dead. I'd try replacing the AC adapter cable first. If that fails to correct the issue it's likely to be related to the power jack or there is another issue such as a failed memory module or it may have even overheated and damaged the CPU.
You can try removing or unplugging the CMOS battery and try it again to see if resetting the BIOS helps. Try reseating the RAM. Aside from those things, if there is no power, there is little you can do without professional equipment to test components.