Sounds like its broken if you ask me.... Though I have never been impressed with the score of reviews for the Dell GPS devices.
I use a Holux M-1000 that I picked up on ebay for about 30$$ and have never had a problem with it, even downtown. Should look into that if no fix.
If the problem really is that it needs low battery before it works then the battery could be over-volting the device... But im not a GPS specialist

Does it have a charging cable or AC/DC adapter that can be used with it? If so, try just using the cable and not the battery.