I gather that you are using the Uniden USB-1 cable since it's the only USB cable available as far as I know. If you are, in fact, using the serial cable with a serial to USB adapter, try a different adapter.
Sometimes people find that another program has taken control of the COMM PORT that they are trying to use to connect to their scanners. Make sure that you have no other software running that might be doing this. Particularly likely are PDA and iPod type synchronization programs.
Make sure that you are connecting directly to a USB port on the computer rather than through a hub. Try a different USB port on the computer. Sometimes the ones on the back work when the ones on the front don't.
There are various drivers out there and some work for one person while another might work for someone else. Try a different driver if possible.
Try it on a different computer.
If none of this works, try finding a computer with a real serial port and use the originally supplied serial cable. This almost always resolves the problem. If it does, you may want to consider buying an accessory serial card for your computer so that you have a real serial port available. Unfortunately, if you are dealing with a laptop, such options are more limited.
There is, of course, always the possibility that the cable is defective or even that there is a problem with the scanner. However, in all of the posts where people have had connectivity problems, I don't recall any where the problem turned out to be either of these things. Obviously, I haven't seen them all, but it's fair to say that defective cables and scanners aren't usually the problem.
Dick