Does the drive show up on your desktop?
You probably need to format it if it is brand new. For it to work with Time Machine, you need to format it as Mac OS Extended (Journaled), and set the partition type correctly.
Note that formatting your drive will erase ALL files on it...
If it is an intel Mini, make sure the partition type it set to GUID, if it is a PPC Mini, set the partition type to "Apple Partition Map". As I recall, you get to the partition setting by changing the partition from "Current" to 1, and then clicking on options.
Set the partition type BEFORE you format the drive.
You do all of this in Disk Utility in your Applications/Utilities folder.
After that, see if it shows up on your desktop, and is available for Time Machine.
Not sure about the "blinking menu bar" part...