MOPHIE is not working

Did you already reset the phone by holding the sleep and home button for about 10sec, until the Apple logo is coming back again? You will not lose data by resetting.

If your battery pack is not charging, check this hint from the Mophie support page:

My juice pack isn't charging.

If both the iPhone battery and the juice pack battery are dead or very low, they may not charge simultaneously if the iPhone is inserted in the juice pack, in this case, the iPhone may chirp intermittently. If this happens simply detach the iPhone from the juice pack and charge them separately.

copied from http://www.mophie.com/frequent-questions

I guess you'll have to contact Mophie support about that, sorry.