How to fix my iPhone [multiple issues]

Ill start from the beginning.

The screen cracked, so i bought a replacement online, i got my partner (who is usually good at this sort of stuff) to fix it, he didnt back up before he did it which im still annoyed about but cant do much about it now.

So he hands me back my phone, it doesnt turn on at all.

I plug it into the wall charger, and it turns on, boots up, everything seems fine.

But then the screens not working, not a single part of the touchscreen works

So i thought id plug it into the computer asap and back up what i could before it did anything else

But when i plug it in the computer, it starts to boot and then loops the apple logo over and over.

I cant get it into the DFU mode to back it up because its looping to frequently.

If i press the home button THEN plug it into the computer it will come up with the connect to itunes symbol thing? and then itunes just asks me to restore which i cant do because i realllllllly need the stuff off it first. Unfortunately, its all baby photos of the first 6 months so ... i seem screwed.

tl;dr

1. Touchscreen unresponsive

2. Only turns on when plugged into the wall

3. Apple boot logo loops when plugged into computer
4. Cant get it into DFU mode

Please help?

P.S. it was jailbroken before all this happened.