3 wires for two terminals?

So it is connected with the fused wire not hooked to anything?

Not sure why it has a 3 wire power connection.....not typical on any Cobras i have owned.

If you are getting out only 1/2 of a mile then something is really wrong.
First thought would be antenna and coax. Then SWR way off.....

The owners manual for that radio shows the normal 2 wire power cord.

http://cobra.com/downloads/manuals/29WXNWST.pdf

 

Solid yellow should be for constant battery feed for radio memory purposes. If you don't want your radio power on a switched circuit (only work with key on) you can connect both red & yellow wires to hot battery stud. Range issues are likely related to swr. Check to make sure coax and ant are properly attached, and not broken or cracked. Ant length may need to be adjusted to get your swr right.

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I don't believe your radio truly has a 3rd wire required. Yes your pigtail may have it though. Some radios do require a constant 12 VDC for the memory. Chances are you have a universal pigtail. Most Cobra 29's don't lose memory when disconnected. It's usually the 18 series Cobras that need the 3rd wire.

When they told you an improper ground could cause range issues, they were referring to the antenna ground. Yes if the antenna is not properly grounded, your SWR will be high and a high SWR is one of the many things that will hinder your range.