Ok, as you've been told, having a car sit is as bad if not worse than daily driving. In this case in particular I don't think the low miles count very much. The ticking could be from valve train wear, rocker or valve tip. If you let the car sit for more than a day or two without running, the oil has a chance to run back into the crankcase leaving the upper head virtually dry. So you start the car with little or no lubrication in the top end, and the first few seconds can cause more wear than hundreds of miles of driving. I'm not saying this IS your problem, but it is a possibility. It could also be a sticky fuel injector. It could be a misfire from a bad spark plug or wire. Could be a lot of things. Is the engine throwing any codes?, check engine light? etc?
I have an '05 4.0 convertible, It's my daily driver. I bought it with 64k miles, and it's had it's share of problems. Like my CD player did the same as yours about 3 weeks after I bought it. I've had fuel injectors go bad, fuel pump issues, thermostat housing leaks (this model Mustang is notorious for this one so watch for it, it WILL happen), and just 2 weeks ago I had to replace the radiator as it started leaking. But I'm also at 117k miles now. And the whole time I've been happy with this car. It's been frustrating at times, as I was new to the whole computer controlled engine world, but I get it now. Oh, and here lately whenever the AC kicks on the engine dies a little but recovers withing a second or two. So I have that to look into now.
Here's what I would do at this point. Drive it for a week or so. Every day, allowing it fully warm up each time. Take it around town, on the highway, just drive it. Carefully record how it behaves, and after a week, come back with your issues, codes, and suspicions, and I'm sure we can help you out further. Don't give up just yet.
Best of luck!