That sounds totally unrelated to the age of the machine, and totally related to what's installed, the mini running out of disk, etc.
Maybe do a clean install of the OS?
Aside from the mechanical parts (CD ROMS, Hard Disks, etc), the "digital" parts of a PC do not age and their age does not affect program execution speed (all other things being equal).
Either they work, or they don't (well, corrupted memory can cause crashes when accessed, but it wont slow down programs).