iPod Touch 2nd Gen with a dead battery will not reinstall OS

### Background ### I have an old Ipod Touch 2nd generation 8GB A1288. The battery died some years ago, but I've been using it perfectly, attached to either speakers dock or a usb cable or a powerbank (all of which provide the power for it run perfectly.) Battery is totally zero. If detached from the usb without power, it doesn't even turn on. Recently I decided to completely reinstall the OS (thinking I'd refresh all the bloatware etc gathered over the years.) Big mistake :( ### What I've tried ### While still attached to the power, I chose the full factory reset option under iOS > settings. The device did some stuff for a while, then it rebooted into recovery mode and threw me a *Connect to ITunes* logo screen. So I attach the cable to a PC (I don't have a Mac) which has iTunes. iTunes says there's an iPod detected which needs resetting, proceed? I say OK. iTunes goes into the process, downloads etc then installs OS and takes a few minutes. After which iPod restarts, but then again goes to Recovery mode and 'connect to iTunes' logo screen... while on the PC screen, iTunes shows error "could not be restored error 1611". Every time (I've done dozens of times, trying with different good cables, and on different PCs.) I then tried various 3rd party tools like 3uTools etc. They all detect iPod, ask me to enter Recovery Mode or DFU mode etc (All I did) and they install it but upon a reboot, they all fail because iPod boots again into the Recovery Mode again. After trying many times, I suspect iPod needs a good battery to reinstall OS. Because when it first reboots after installing the OS, it fails to do or detect something which requires a battery? By the way, 3uTools has an option where I can see what songs or apps are in iPod, and it shows the list as if everything is still all there! Apparently just the OS is not there for some reason. ### Question ### Is there anything else I can try without having to install a new battery (which I don't have any experience of and I might break the device.) I am hoping for a software only solution here.