indeed, you would have to find a processor, and then find one that is faster than your current one, practically destroy your laptop to change the processor out, and all that to get such a small performance gain that you would not even notice the difference.
A better, and easier, upgrade would be to max out the Ram available to the processor, and put in the fastest/largest PATA HDD you can find.
All that said, for what you could find the HDD and Ram for you could purchase a new entry level laptop that you would be very happy with compared to the old P3.
While I am not personally a fan of Dell, I know 3 people who have bought this model in the last year, and they all seem pretty happy with it:
http://www.dell.com/us/p/inspiron-15-intel-n5040/pd?p=inspiron-15-intel-n5040&ref=aInspN1B
If your P3 lasted you 13 years, then I am sure that one of these would do the trick for at least another 10.
Those old P3s were damn near bulletfroof wern't they! Where I work we get them donated all the time, and there are a great deal more of them in working condition than newer P4's. They were never particularly fast, but man were they made well!