Monitor will not stay on

I'm afraid that most probably your monitor is failing. Try to connect it to a different PC and see if it's still blanking.
I've had few cases of dell monitors dying in similar manner to yours. In all cases it was caused by blown capacitors on the logic board in the monitor. (overheating/poor quality components). Once replaced, the monitors were back to life and are still in service today.
Of course unless you like to tinker with electronics this is probably not worth repairing as the monitors are fairly cheap these days.
Hope this helps,
Raf