The equipment required to properly test a digital cable signal - not just the presence but the quality of is expensive and is unlikely to be something you would want to acquire. If a temporary cable runs works correctly then it would seem like the technicians assessment was correct, especially if it is run from the same splitter as your other line.
The existing cable might show continuity (i.e. there is no physical break), but if the cable or terminations are damaged then you will not be able to utilize this run.
Typically I would replace both ends of the cable before doing any further troubleshooting as these can pull off the cable if not installed well. You would also want to do this on the end of the cable that connects to the other side of your wall plate, and where the cable connectors to the splitter.
As for the unsightly cable, you could either get the cable company back to run it nicely, or if that is not something they will do (a lot of times they will not do any in-house runs) then you can contact an electrician or cable installer (alarm installers will often do this too) to run a new cable in your walls if it is not something you feel comfortable doing.
If you search for running cables on this site you will find some information on how to do so.