If the power led goes on then this means that your CPU is running.
But i agree with the others remove everything except the barebone A1200 and try again. The plug in the stuff one at a time and find the point of failure. This also include your harddrives!
If the problem persist, check if the monitor is even working. I have once tried that a shorted monitor cable fried my graphics card (on a PC (but the problem is same for the Amiga)).
Finally check the power supply.
If all this fails, then you *may* have a defective motherboard. Then only three choices persists: change the motherboard (a1200), find someone who can repair it or spend a few weeks not finding the problem (i have done that with an A4000).
Best of luck
