ipad won't sync and won't charge unless fully discharged

My first-generation iPad will no longer charge at all unless it is fully discharged (charging by wall plug or usb to mbp). Even then, if I plug it into my mbp, it charges but is unrecognized by iTunes. it DOES sync over wifi, so that hasn't been a problem until now - when the OS needs updating which can only be done by wired sync.

So here's my question:

how can i fix this? should i do a full restore of the iPad, plug it in and pray that it works? if it isn't recognized i fear i will have demoted this device - which is still useful at least as a toddler toy - to the bin of fun things for my son to hit with a hammer.

thanks for any help!!!