Unplug the system, remove the base cover and disconnect the battery from the system board. Hold the power button for 30 sec.
Plug in the AC adapter (battery disconnected) and see if the system will power up. If it will, shut down, reconnect the battery and try again. If the battery halts POST, it's bad.
The eight beep sequence usually means a system that does not sense the display panel. That could be a bad display panel, but can equally well mean a bad system board. One way to test is to hold the D key through powerup. If you see a series of test screens appear, the screen is likely OK, meaning the fault is with the system board. If you do not, it points to the display being bad (but does not rule out that the system board could be faulty as well).
Depending on the system model, it may or may not be worth a major repair such as a replacement panel or system board.