[Q] Note N7000 afterlife? :)

Hello, dear people at xda! :)
Unfortunately, my dear Note seems to have a busted battery, as when I fully charge it and try to go on internet (3g, not wifi) the phone starts to flicker and turns off after 10 minutes of connection...
I tried reinstalling different roms, but it is defo the battery....
and since it is a 2 year old device, which I was planning to replace some time in spring 2014 anyhow, I am not seeing any sense of buying a new battery for it.... Therefore I will just go for a new(er) device (not sure if Mega 6.3, or Sony Xperia Z Ultra)...
However, I am not sure what to do with my Note N7000... Selling it like this, I doubt anybody would want it... and plus, the exterior has got some damage on corners from falling, grazing, etc...
I was thinking of having the Note N7000 connected to a power source without the battery in, and hooked up to a 15 inch monitor, and mouse and keyboard and set it up as a quick email check, light browsing, etc, machine...
I have seen on the internet some people using android phones like that, even if just for experimenting..
I like my Note very much and would hate to throw it in the rubbish bin... I think there is still some use I can put it to...

Any thoughts?