As you say it is a Duo 2.4GHz CPU, I'm assuming that it is a Core2 Duo E4600 2.40GHz. That being the case, it is pretty slow by today's standards and upgrading other components may make little improvement.
However, depending on your operating system, adding more memory may help (and is a very inexpensive, quick and easy upgrade). If you are using Windows XP, then 2GB probably is enough unless you are into heavy applications (big time gaming, video editing etc.). But if you are on Vista / Win7 (especially if they are the 64bit versions), then upgrading to 4GB may make a noticeable difference as your system could be paging a lot, with high disk activity and slowing things down).
Also, as you say that you are having to delete old apps to install newer ones, it suggests that your disk could also be a bit of a bottle neck as disks do slow down as they approach full.
For around £250-300 you should be able to get a a much more powerful complete system unit (that price is without operating system).