Pete, the bike battery supplies 12 volts which is dropped to 5 volts to charge the GPS via the mini-USB connector, so charging from either a wall socket or the bike should make no difference to whether it is working correctly or not. Take a look at the charging indicator when plugged into any of the three sources (bike, mains or computer) and make sure that it shows it actually charging, if it isn't then the charging circuit in the GPS has died. If it does show it charging then leave it for about 12 hours with the thing turned off so that you get maximum charging current to the battery, then try it again.
I have a GoCruise 1602 and it has a LED on the front left side of the unit which glows red when charging and then turns green when fully charged. If the LED hasn't turned green inside 12 hours then the internal charging circuitry or the battery have died. As a tip, when you plug the GPS into a computer USB socket when its switched on it should, after a few seconds, ask whether you simply want to charge it, or whether to use the GPS as a mass storage device, i.e. you can upload and download stuff to or from it. Either selection will charge the battery, which should then give you about 4-6 hours of use before it runs out.
If the charging thing isn't happening, then try the hard reset option, and if that doesn't work you will have to return it to the supplier, although it's probably easier to throw it in the bin and get a new one.The GoCruise is quite cheap anyway and a new one gets you all new maps and the latest software, so not a complete loss.
Hope this helps
Cheers
Whizz