E-Monster 600 won't shut off.

It would help if you indicated whether or not this exact configuration ever worked. I will have to assume that it was once working and that nothing changed (like added hardware or software) before the error condition presented itself. In that case, I would suspect a faulty power on switch. If you had a multi-meter you could set it to Ohms reading, disconnect the on/off switch from the motherboard and put one lead on each of the two pins. They should be open in the off condition. Try depressing the switch. The meter should change from the open condition to a short. I suspect that the switch is always shorted.

As for the monitor and DVD problems, they sound like a different issue, or else the motherboard is shot altogether. In any case, you will want to find out first why the power-on switch isn't working. Once that is resolved, and if the other two problems are still present, I would remove one of them from the equation, preferably the DVD drive, by disconnecting from the motherboard AND power supply. If all comes up normal then the DVD drive is ad (not an uncommon problem, actually). If the monitor still doesn't come up, and if you are using a video card AND have onboard video available (if you have a 15-pin video connector on the motherboard then you have on-board video), try removing the video card and just going with the onboard video. If this works then it is likely you have a bad video card. If there is no on-board video, try using a different video card (a friends or one from another computer). If none of this fixes the problem you might want to try replacing the power supply as it could be under performing and just not giving the motherboard enough "juice". If even that doesn't work then I would say your motherboard is toast and needs to be replaced.