Trackpad and USB power Issues

Hi, i recently got a Macbook Air model a1237, i'm really enjoying this computer but it came with several issues, first, there is no battery so i have to run it from the power adapter.

I think the machine underclocks to 800Mhz without the battery so i don't complain about the computer being slow, but i am thinking this can be the source of some of the trouble i have now.

First and most important to me, the USB port constantly stops working, i get an alert of a usb device taking too much power and that it must be disabled, and then anything attached to this port just stops working this happens way to often and when using my bamboo tablet for photoshop it's just impossible not to mention what a headache was just to get Snow Leopard installed.

The second is the touchpad, if i use the touchpad touching only the touchpad it just makes random movements and clicks is just unusable, but as soon as i put one finger on the metal casing of the computer it just works flawlessly as long as i am touching the metal while using the touchpad it works fine.

So i was thinking it may be a lack of ground that the battery can supply but i can't know since i have no battery and i don't really need one because this is not my main laptop, i wouldn't want to waste money on a new battery that i don't really need only to find that it solves nothing.

Please if someone has encountered any of this issues and know a way to work it out, let me know i do appreciate it!