how old is your computer? If you have a lot of songs I highly recommend upgrading the USB to 2.0 if you don't actually have it. You may have it, just not the right drivers installed. If you don't have USB 2.0 then it will go INCREDIBLY slooooooow on the songs transfer and maybe even cause issues syncing with the computer.
First thing to know about ipods, a lot of people will say they are junk blah blah blah. I own a ipod and I fix them all the time at work.. I don't think they are junk at all, I just think they get abused and are tempermental, and people just don't know how to woo them lol. The software on the ipod can corrupt and cause all kinds of problems. If it's giving you issues the best thing to do is to restore the software and make sure you have the latest version of the software. This can all be done in iTunes 7 now. about 9/10 ipods that come into my work I restore the software and upgrade and it fixes the problem, simple as that. Like I said, they get abused.
If your ipod looks up or you just want to reset it hold the select button and the menu button together until it resets. You can enter diagnostic mode by doing this and then when the apple logo is displayed you press the rewind and select button and hold. Diagnostic mode will let you test the physical hardware of the ipod.
Now as far as your computer not recognizing the ipod, look under My Computer or the Device Manager.. the Ipod will show under both of these. If its not listed in either there maybe a hardware problem somewhere. I have seen computer problems that cause this, for example they dont install the driver for the ipod properly.
Good luck!