Can I replace a Celeron-M with a Centrino?

That's going to be an incredibly tricky job, and most likely getting it done for you will work out considerably more expensive than a new machine. However:

I'm not positive but it should be possible as long as the CPU/motherboard socket and bus speed etc are compatible. (Whether any centrinos were made with the same socket as Celeron-M's I honestly don't know). What is the exact model of motherboard? You can find this most likely through the Dell website by throwing in your service tag in support. All you need do when you have these details is check the specs online (preferably through the manufcaturer's website) and ensure they match, or post them up here and someone will give you an educated opinion.

You need to make sure you're not putting in a CPU that will draw a lot more power than the original, too, as laptop PSU's I can only assume will not cope well with overloading.