CPU fan for Celeron D 340????????????????

My new CPU is Celeron D 340 2.93GHz socket 478 256K L2 533MHz FSB. My previous CPU was P4 1.7GHz socket 478 northwood 256k L2 400MHz FSB.

Is my previous fan compatible with my new CPU? If it does, will it work well on the new CPU? If not, what's a good & cheap fan for my new CPU? (multi-socket fan would be the best)

Your old chip had a TDP in the 45 watt range. Your new chip would be close to double that, so NO, your old hsf is way too small.
You can usually pick up a stock fan for a P4c 3200, for about $10. That should do the job nicely.