Computer Problem... It won't turn on!!!

Probably a problem with the power supply or the motherboard. If you can open the case, you can try to reset the board bios. With the system off, either remove the board battery for a few seconds, or move the "cmos" jumper over one pin position, and return to the "run" position with the power supply unplugged (it's a 3 pin cluster usually near the battery). Either method will work. If nothing changes, then you have to decide if replacing certain parts by trial and error will fit your budget or timeline, or if you want to order a new pc. Want help with parts, then list a budget and your system specs, starting with the motherboard model number, cpu, and memory. But first, try a different monitor just to be sure. Mine died a few months ago; probably a backlight problem.