Quoting me was very touching, thanks.
Anyway, Tim, completing things is indeed a skill that needs to be developed. If you want to complete projects, you need to practice. You should definitely write something for this contest even if it sucks.
In my experience, there are generally three main reasons people get writer's block.
1. Lack of commitment. Writing is very hard, and every story idea you have will be broken in some way. Generally when people get to the point where it's not fun anymore, they start fantasizing about working on some other story that will surely be better, and if they are weak they succumb to the temptation. You need to stick it out even when you feel like it sucks and no one will want to read it. To be honest, this is probably true when you're less experienced, but the only way to get better is to tough it out and keep going.
2. You get in your own way too much and can't stop self-censoring long enough to spit something out. The solution to this is twofold: an iterative drafting process and writing drills designed to make you spit out words as fast as possible. I like drills where you try to write as many words as you can in half an hour or so, accepting that they will suck, with the only measure of success being how many words you wrote. It's fun and motivating to do this with other people, too. You can turn it into a contest where whoever writes the most words is the winner.
Anyway, accepting that your story will require multiple drafts frees you from the obligation to write something good the first time, which is very helpful. I'm at the point where my rough drafts often read like detailed outlines with dialogue, which is great because I can skip all the unfun parts and don't feel bad about cutting entire sections during revision if I think they're not working. Once the general shape of the story is good, I'll go back and add all the details.
3. Something is legitimately wrong with your story. When I get to a scene I just can't write, I step back and try to figure out why. Usually there's something wrong, like there's not enough tension or conflict in the scene, or some plot point didn't work out like I'd hoped. Identifying the problem and making the change is usually enough to unblock me.
If you haven't planned out your story yet, I would start by doing this. Start by figuring out your ending, which is by far the most important part of the story. After that, figure out your three-act structure and write an outline.