Hmmm....
Very interesting.
1. It sounds like someone jumped the fuel pump to come on with the key. Not to smart, but that's what we are working with.
2. Your car not running doesn't sound related to the fuel pump being on all time. Do you have spark? Pull a spark plug, hold the tip to ground with an alligator clip jumper and crank the engine. If no spark, it doesn't matter that you have a fuel pump running all the time, fix the spark problem first.
3. If you have spark, do you have fuel pressure? I have read that the fuel pump may sound like its spinning, but not producing any pressure.
Let us know the steps to fixing you have taken so far.
-Michael