Should I just buy new computer?

1. Mouse no longer works
2. WiFi no longer works
3. With AC adapter unplugged, no battery icon appears and it says I'm still plugged in.
4. Left AC adapter plugged in overnight to charge battery. Next morning battery/netbook was not even warm.
5. Still able to power on Aspire One and use (with no internet) on battery power alone.

My AA1 with Linpus Linux Lite is four years old.

 

Well I'd think about this...
10400mah chinese battery off ebay (mines fab) £40
new pcie wireless card £10 http://cgi.ebay.com/Acer-ONE-ZG5-Wireless-WIFI-Card-T60H976-11-TESTED-/180600109774
usb mouse £8
linux mint 9 free

follow this excellent modding vid to replace the wifi card
http://qik.com/video/161904
which is very easy and for just short of £60 you'll have your baby back and it'll run for 9 hours plus. Not to mention the fact that once you've been "under the hood" you'll see just how easy it is to service these things and replace bits generally. Main tip for modding is get the right size screwdriver and use the palm down pressure on top of it and turn with pliers as in this vid
I would open her up and providing you dont mess up any of the screws, which is sometimes problem, I'd give it a whirl
Luck to ya

 

That could be a software setting, mouse battery or hardware. Thus needs trouble shooting before using it as a decision point.

Did you check the switch position? Did you try and remove the software WIFI connection reconfigure it and connect it again?

Did you try leaving the computer on until it shuts down and then recharging the battery? This sometimes resets the calibration of the battery.

Mine never gets warm when plugged in and charging.

Do you mean that your computer will not power on if plugged in to AC power?

I would recommend you switch to Linux Mint 10 from....
http://www.linuxmint.com/edition.php?id=69
It is the one I use and everything I use works perfectly with it.