If I'm right, that's a single-threaded Core Duo, i.e. not even a dual thread C2D. No wonder it's slow.
Also I wouldn't have put Snow Leopard on it. SL really does need 2GB+ to shine. 1GB is far too little. Have you considered down-grading to Leopard or even better, OSX 10.4 Tiger?
Check your software - almost everything that works with SL will work with Leopard, but with Tiger you may need to figure out how to replace a couple of apps.
On that model of Mac Mini, Tiger gets higher Geekbench scores than Leopard, and as the computer was released with Tiger, it will happy with Tiger and 1GB RAM. (1GB is double the 512MB the computer was released with).
A good reason to avoid Tiger for Leopard would be if you use Time Machine, which is brilliant but not in Tiger. Other ways to backup on Tiger:
https://getsatisfaction.com/apple/topics/what_is_an_easy_backup_solution_for_os_x_10_4_tiger
So your options:
Free:
Downgrade / reinstall the OS.
Turn off Spotlight (via Onyx or similar) & Dashboard
Turn off as many background services as possible (via Onyx etc)
Remove as much software as you can, especially software that modifies the OS. (or reinstall the OS and only install what you really really need)
Turn off screen savers, desktop background etc.
Low cost:
Cheap SSD (and use your current HD in a USB / Firewire (better) enclosure)
More RAM (2GB)
Replace the processor with a C2D
More expense:
Sell your two systems, and purchase a second hand but newer Mac Mini or a Macbook. I recently bought a 2009 Macbook with C2D 2.2GHZ, 500GB HD, 4GB RAM, Radeon 9300 discrete graphics, for £350 from eBay, and I'm very happy with it.