This kind of struck a chord with me, at least the part about nothing going out. I have one full short story written, one in progress, a bunch of ideas laying around on note cards, and a novel I've finally started working on. I've always had a problem with (as one person put it) "the bear". I feel down on myself until I just don't want to try, so I don't actually do the writing. Ok, sorry, so that was about me... this comes back to the topic below, I swear!
Fortunately my complete short story had already been critiqued, edited, reviewed, etc. So I sent it out. We'll see what happens, but just doing that seemed to free me up. It's in limbo. Maybe I'll never get a response, and it doesn't matter. For the last 2 weeks, I've finally felt free to write the novel that's been brewing, because I'm trying to get out there, instead of just thinking about it a lot, and I've been able to get much more work done than in the previous several YEARS!
I also don't think that there is anything wrong with switching tracks now and then. Basically what I'm saying is that it probably is a good idea to finish your draft first, then let it lie a few months (that's common advice). That's the time to work on some short stories. Get your ideas out into a more fleshed-out format, and see if any of them start to take you somewhere farther. These are just some thoughts, but the more samples you have, the more likely someone will pick up your screenwriting too. Whatever your format is, though, "shorts" are good for exercise and experimentation. Shorts are also a lot easier to get published, and you can try a lot of different things with them.