Chosen Solution
Primary Symptom: •The Fan runs loudly at full speed, and stays on all the time, as soon as the computer is booted. Other Symptom(s) or Details: •All operations of the machine seem to be slower than they used to be, whether using just the OS, or running an application (I do not know if this is a related problem). •80GB HD with 47GB free space. 1GB RAM installed. Computer is used only for email, internet browsing, and to run Finale (music notation software - no audio processing)
Possible you forgot one cable in the back of the Mac Mini.
Download, install and run TG Pro to be able to locate the problem: https://www.tunabellysoftware.com/tgpro/
Heat sinker must be cover with thick dust and the fan is working overtime to keep it cool. Open unit and with a compress air can blow it clean. Some of the current drawn by the fan pull resources from other components (CPU, video, USB, etc…) slowing everything else.