Maybe possible, but I would say not worth it. Even the best CPU you can get for that system (on paper) is pretty slow compared to anything made in last 8 years, and even if the CPU fits in the same socket it may not work. I'd spend $150 and just replace it with a older i3 or i5 laptop. You can find things like T410, T420 systems for well under $200.
You can also just try a clean Windows setup on a new hard drive, solid state would be best, but then you are spending about $40-50 on a system that is just slower overall vs a newer full faster system.