Well you might experience crashes, performance loss, and if it does crash you could have corrupted memory in your HDD. Or possibly have hardware failure and have it need replacing in the worst possible circumstance.
I would honestly consider moving to 400 or 500 since 300 would not meet the requirement for your full computer.
could i run it with 300? thats the best supply i have laying around, the house i could get a 400 though