Yes, with an unexplained high SWR reading you need to rule out a short in the coaxial cable. It's not uncommon for poorly or incorrectly install UHF connectors to do this.
So, here is a couple of other things to check, since it sounds like you've done the basics:
Remove the whip from the antenna.
Check for continuity from the center pin on the bottom of the coil to the point where the whip attaches. You should have continuity there.
Before you reinstall the whip, do the following:
Use a file, knife, sandpaper, teeth, or something to remove the whip coating down to bare metal where the set screw hits.
Make sure the inside of the "cone" where the whip inserts is clean and not corroded.
Make sure the set screw is clean and not corroded.
Make sure the threaded hole where the set screw goes is clean and not corroded.
When you tighten down the set screw that holds the whip in place, make sure it's tight enough to make really good contact.
The spring loaded pins on the bottom of the coils can be problematic. Make sure it moves freely and isn't jammed up.
Sometimes certain NMO mounts and certain antennas don't get along. It is possible that the center pin of the coil isn't making contact with the NMO mount. When I see your picture of the NMO mount, I can see that the outer threaded ring is sitting higher than the inner part of the NMO mount. This can create issues where the center pin of the coil won't make contact. You might need to disassemble the NMO mount and make sure there are not any extra gaskets in the way. Some of those ham radio brand NMO mounts are designed for half wave antennas and they don't put a lot of effort into making sure everything is grounded correctly.
-as for those above steps, it's a good idea to check those often. It's pretty easy for water to get down inside where the whip attaches and can cause corrosion and no end of issues. Antenna preventative maintenance should be a regularly scheduled thing.-
Reading through your previous posts, you guys look like you are on the right track. If you were local, I'd happily give you some of my time to help sort this out. It's likely something simple to fix it.
Not likely it's the radio. The radio will put out a carrier, or it won't. If your SWR meter is moving, then it's putting out a carrier.
Can you give some info about your SWR meter? Is it the one built in to the radio, or are you using a stand alone meter? How are you setting it up? How are you calibrating it? If it's an external one, how are you hooking it up?
What about the coaxial cable? Is it the stuff that came with the mount? What about the connector? Was it pre-installed or did someone install it?
Is it one continuous run of cable, or did you extend it?
How are you powering the radio? Where is your power coming from? Is the body of the radio grounded? (don't rely on the negative power wire for this.)
hang in there, these things are not that complicated and we'll help you sort it out.