HD in target disk mode won't mount

So I'm caught between a rock and a hard place....

I have a MacBook Pro thats a couple years old (obsolete according to Apple...) that runs great and not full of apps music or files.

While updating my MacBook Pro to the newest version of El Capitan the laptop wouldnt restart. Come to find out it is some sort of limbo between updates. I shouldn't have memory storage issues but in first aid it shows that capacity is full. I've been to the Genius Bar and they suggested after trying a couple fixes that I copy files and reboot the computer after creating a disk image. (I got an error code for input output). I can't reboot in time machine because I wasn't prepared for a shut down and havent backed up due to lack of storage space. I have booted up in target disk mode but it won't mount to my Mac mini. I've seen the drive in terminal under diskutil list as well as system report on the mini. It comes up in disk utility but the drive won't mount. I feel like all the files I have stored on the laptop will be caught in this limbo world until I can access and copy them!!

Where does that leave me?!?

Back to Apple for a genius bar appt?? Will it ever mount or allow access somehow?