My motherboard doesn't seems to work

video card then see cable as well

Usually you have to toggle the display output on the laptop. The FN key + one of the F# keys with a monitor icon on it. Toggle it until it outputs to the monitor. Your getting "no signal" because no signal is being sent to the monitor or you have the monitor on the wrong input if it has multiple inputs.

MB was shorted. Probaly ruined it
No ever work on an MB if power is on

Is the monitor new? Because some monitors need to warm-up a little bit. Have you tried to remove video card and/or mother board and reinsert? If that doesn't work, try the video card in another PC, If it works there, then the video card itself is probably not the problem. (recommended). And those beeps (3-3-3-1) mean "Erase F2 prompt", but I don't know exactly what that means. This is all I know for now.

If you hear the CPU fan turn on that doesn't mean the CPU itself is working. It can be only that the motherboard is getting power. Check all your connections such as monitor and peripherals and re-connect them. If you still don't get P.O.S.T. or ANY letters or boot options on your screen then your CPU is dead. (unless your monitor is bad)
Another easy diagnostic is using your ears. For example the pitch sound of the fan in some motherboards tends to lower and then increase because it's reading of the hard drive. This means your CPU is ok but either your graphics connection is bad or your monitor is.

Check your cable between the computer and the monitor, It may be a non-sensing cable which will be missing one of the pins so the monitor is not getting the correct data from the computer.

So either the computer isn't generating a video signal, the cable isn't carrying the signal to the monitor, or else the monitor isn't capable of receiving a video signal.To test this, first try a video cable that you know is good, in case your cable is bad, If it works with the other cable, the problem was your original video cable. If it still doesn't work, put your original cable back, and hook another computer up to the monitor. If the monitor makes the same message, the problem is with the monitor. If the other computer works when connected to this monitor, your problem was that the original computer isn't booting (which could be due to several reasons I will list below), or the video adapter is broken.Possible reasons for the computer not booting: bad power supply, bad power button, bad hard drive, bad memory, bad motherboard component. If you determine that it isn't booting, unplug everything except the keyboard mouse monitor and power cord, to see if that makes a difference. If it boots after that, something you unplugged was causing the problem, plug them each back in one by one, rebooting in between, and when it stops booting properly, the last thing you plugged in is causing the problem.

First, be sure to check the data cable which runs from the monitor to the computer. Verify it is connected. If this does not fix the issue, then the problem is the result of one of two things:
1.) Your monitor died and needs to be replaced. You can check this by plugging the monitor into another computer. If it works, then the issue is not with the monitor and you will want to move on to #2 (below). If it doesn't work, the monitor needs replaced.
2.) Your computer is not sending a signal to the monitor. This is an issue with either the video card or motherboard (most motherboards have the video card built right into them). You can install a stand-alone video card and see if that solves the issue, but chances are you'll be having another motherboard installed (as well as having to have Windows reinstalled). If you have never done this, I would recommend a computer shop.
I hope this is helpful and best of luck!

Test the card with another monitor first of all
I seem to think that this card requires a connection from the PSU ( check if there is a connection that would take a 12volt 4 pin molex or a floppy drive type power connector on the card)

Also, you should be running at least a 550 watt psu

If you saying "doesn't always boot", most common would be motherboard...
If your motherboard still beeps, then probably some other components has the problem like RAM, GPU card etc., depends on your motherboard.

Hope that give an idea...