The single best thing you can do to any computer is change out the hard disk drive for a solid state drive (SSD). Especially now, as the prices have been steadily dropping over the last 18 months, and have stabilised recently.
I recently did this to a 6-year old Fujitsu-Siemens Amilo 1718 (a cr@p laptop when it was made!, 1GB RAM and a slow Pentium4-based processor). It had got to the point where it was barely usable, and very frustrating. Once I'd put in a £45 60GB Samsung SSD, it now flies for all the usual laptop stuff - web browsing, some office applications, streaming video either from BBC or over the network. The boot time is stupidly short, as are the sleep and wake-from-sleep times.
It can be a a pain to get your data from a large HDD to a smaller SSD, but there are places online that are very helpful, provided you can still get online (ie is it your only computer, or can you browse on another machine/phone etc).
It's worth having an external USB disk that's large enough to write all the data you intend to copy (if it's an HDD, this won't be an issue!), and a 2GB+ USB stick to put on the bootable software to enable you to clone the drive. I can dig out the links I used if you decide to go down this route, they were very helpful!