iPhone after battery change in dfu loop. Data recovery still possible?

Hey guys, after 3 years my battery died. I bought a new one on ebay and replaced the old battery(done it before, also with a different 4s and it worked out). It charges now but the phone stays in dfu mode(charge+itunes symbol on display).

I tried to update it with Itunes but thats not working either(Error 21). Reset is no option, because my latest backup is outdated and I dont want to loose my data, pics etc.. On iCloud is no real backup too. I also tried the Home+Power Button method, a variety of programs(tinyumbrella, update with jailbreak) and the outcome of my efforts stayed the same/the software said its not working in the current mode.

I just want a backup of my phone´s data, if still possible, or as a best case scenario a working phone. So is there a (free) software I could use or a similar possibility to restore the data?