If you go and get a new network card then it will run at the standard LAN speed of 100Mb/s which is quite fast and the system should be able to keep up with that. If you get an el cheapo harddrive and fit it in then you can use it as a nice networked storage backup box and it will do that job at pretty much the full speed.

As for the CPU processing power - its not worth trying to get any more out of it. Its a fact of computing that your old machine is many many times slower than your new one.

If you run a VNC server on the old box then you can run a VNC client on the laptop and view the screen on the laptop. Also if you buy a projector or have a large monitor for it then you can use the old box as a projector / map slave for VTT's when playing RPG's