Not the external speakers. There is a four-pin header on the motherboard that should plug into a small internal speaker. That speaker is used for the POST codes.

Any true dual-core is going to be faster than a P4. If you have HT enabled on your P4, it will almost act like a dual-core running at 1.6G. (Not quite, in that one thread must volunteer to give up its half of the CPU before the other thread can run. SMT as used in the Core i7 allows both threads to actually run at the same time on one physical core.)

Multi-core machines just work better. One thread can hose a single-core machine, whereas with more than one you have some cushion.

For power requirements, you need to add up the wattage of each part. Perhaps you don't have enough, but I would expect a P4-based machine to run at less than 450.

However, this brings up another question. Are you sure that your power supply is good? I've only had one CPU fail on me, ever, but have had many power supplies die.