For example, HAL is a resource hog in low-end systems (polling daemons--).
Depending what you need to do, you can
those daemons. That doesn't affect online access, at least not in Mepis. Use command
to find the PID's of the daemons.
I'm running Mepis 6.5, though ONLY to get online with Firefox, with a 2001 machine: About 1k Mhz, CD-ROM drive, Ethernet card, speakers, old LCD monitor, and 256RAM. Even uninstalled (no HD) and running from CD, I can sometimes use Kate or Kedit, as well as multiple instances of Firefox, plus Konsole. With very fast cable access, this works fine as an online-only machine. Can even watch a few youtube videos now and then. Is your machine older than this?
Mepis 6.5 can't run from an equally old Dell laptop I have, though, most probably because of insufficient RAM. If you can find a used-PC store, you might be able to scrounge RAM fairly cheaply. Otoh, once I accidentally left a USB key plugged into a PC when I tried to boot Mepis from it, and the system (from CD) told me it was going to use it as additional RAM, so you could try that -- probably $10 or less for at least another 512Mb.