[cpu Upgrade] Need Help For A Cpu Upgrade

Hi everyone,
I have an Acer TravelMate 800 laptop, which I disassembled and that I want to use as a "secondary PC" just in case I need a computer for something. Now, it has an Intel Pentium M clocked at 1.3GHz, 512MB RAM (128MB + 256MB) and a 40GB HDD (4200rpm). As you may expect, the performance are... Not so brilliant. I've decided to upgrade the RAM to 1GB (which I have fortunately found compatible with this very old PC) and the HDD, replacing it with a faster one that has a rotation speed of 7200rpm. My question is: it's even possible to upgrade also the CPU? I have made some research and I have found that the motherboard uses the Socket 479 and the chipset is supposed to be the Intel 855PM. My questions are:
1) Can you confirm that the chipset (not the CPU) is the same for all the versions of the TravelMate 800? Here it says that there are three versions with three different CPUs, and I don't know if my TravelMate is the 800LCi, the one which the specs previously linked refers to.
2) I think that the Intel Pentium M 780 can be a valid CPU replacement, but I have no idea if it can works with the motherboard. Just in case, it will downclock itself or it can mess up everything? Thanks in advance for your time.
Simone Sola