What does "Boot Loop" mean? Are you saying it starts up to some point, and then resets (shows Apple logo again).
Can you get it to go into Disk Mode?
Putting iPod into Disk Mode - Apple Support
If you can, run iTunes and connect iPod. If iTunes picks it up, it may prompt you to do a Restore with a message about "recovery." Tell iTunes to proceed with the Restore, which erases the iPod, installs its software, and sets it to default settings. If that does not help...
The "micro drive" is a tiny hard drive that is no longer produced, so that one you acquired is likely to be used. It may be faulty, unless you have tested it using a different connection that does not involve the iPod. The internal connector for the drive is the same one use by the common Compact Flash format. You can use a standard CF card in your iPod mini (although some may not work for this purpose). You can also use an SD card to CF card adapter, and use an SD card in your iPod mini. SD cards tend cost less compared to CF card, for the same capacity.
I have an iPod mini with a 64GB SD card on an adapter. It is the earlier model (like yours) which originally had 4GB storage. This is the adapter I used
http://www.amazon.com/gp/product/B00EPMWT1M
CF card does not require an adapter; if you happen to have an old one, try putting it in your iPod mini as a test.