My dell dimension 5100 will not power up

HELLO THERE:
The first thing you should do is to see of the power supply is working or not if not replace it if it is and you are sure that it is than i would open the case and make sure that all connections are tight by pressing firmly on all of them
If still nothing unplug the harddrive and the cd rom from the motherboard and see if it will power up now if so reconnect the harddrive and see if it will now boot if not check the flat ribbon cable to see if it is damaged or is not connected fully than repete these steps for the cd rom ok? try each one seperatly to see how this works if it is now than you know what is wrong ok if not leave the harddrive and the cd rom dissconnected from the motherboard than unplug the powersupply cord that goes to the motherboard and press the power button for 10 seconds and than press in the reset button if you have one for 15 seconds now plug in the cord from the power supply back into the motherboard
and turn on the computer it should now at least come on if still nothing your board may have failed or your power switch may be faulty ok I hope that this hass been very helpfull for you
best regards michael

First and foremost, since "this has been a recurring problem since it was new," is it still under warranty? That's the simple solution. My next step personally would be to unplug everything from it, and VERY CAREFULLY re-seat all cables you can see and the RAM as well, but only if you are comfortable doing so. The parts of a PC can be very fragile.