mac mini 2010 usb-harddisks are not booted
Our Mac mini (mid 2010; OS 10.11.6) stopped to recognize several external USB-harddics (including the shortly before used time-machine-drive) that work fine at other macs. It is therefore not an issue of the discs (or the cable). The disc utility program shows the harddisc, yet not the volumes (or their name) on it, and first aid program is not checking the volumes. However, usb-sticks work normally. I first thought, the power supply of the ports would not work, however the CD drive (apple superdrive) works also fine. Resetting SMC and PRAM had no effect.
Any idea what could be wrong and how to fix it?
Mac mini, OS X 10.11