While there is plenty of reasons your old laptop to be slow or freeze, I would tell you about one that might not be so obvious.
I came across this issue 2 times in the past months and I decided to share it, because it might be useful for you.
It turns out the issue with bad performing laptop can come from inadequate power supply, and more precisely from the laptop cable or cable connector.
Here are two examples where I came across this issue:
Lenovo T500
This laptop can be running extremely slow, but it will not overheat.
This model comes with 20V power supply and cylindrical connector. Its very common for the cable to start to break near the cylindrical connector from the years of flexing. Look for exposed wires near connector, if thats the case you might consider replacing the power cord. Sometimes outside layer of wires inside of the power cord can be broken off even if no wires are exposed. Bulge near the connector is sign the cable is starting to go bad.
Lenovo G560
This models can start freeze. They are equipped with external video card and its normal to run at slightly hotter temperatures. Before start thinking of thermal compound replacement check the power cord connector! Dirty metal leads can reduce current flow which will cause the laptop to crash on high load. If metal leads are partly broken off laptop may power off when you fiddle with the connector. In that case you might consider replacing the cord.
This sums up my experience with faulty power cords of old laptops.