Sometimes, you'll find that a plug's come a little loose, or it operates right only when the plug's being pushed in one direction. Flexing the cable doesn't change anything, but moving the plug seems to always fix it (or break it).
Odds are, it's a broken solder joint, or a broken trace on the motherboard. Either way, you can fix it with some soldering.
There are a lot of online tutorials about soldering, but if you're just starting out, keep reading a bit more. Links are at the bottom.
First things first - there are only two irons to get. One is the Radio Shack low-voltage (18 W I think) lower temp iron, which has a conical tip. That's my favorite one - it doesn't get things too hot. Second is a 30 W "cheapie" iron with a longer tip that ends in a cone. This works hotter, and is better for heating stranded wire.
For now, stick with the first iron. It's a little rare, but you can get it at radio shack.
Second, get some solder. I like the thin lead+tin solder. It stays soft longer, so it's easier to work. The lead-free, safer one, is harder to use. The type of solder to get depends on the existing solder. You shouldn't mix the leaded with the unleaded.
Lead-free is a lot harder to work with. Read up on it.
Third, get a desoldering braid. This is a copper braid that you put on an existing joint, and heat up. The solder joint will melt, and most of the solder will be sucked up into the braid. Then, you can remove components, or start a new, clean joint.
Fourth, get a cellulose sponge. You can find big yellow ones at a home improvement shop. Cut it into smaller sponges the size of a bar of soap. Soak in water and wring out. When you're soldering, you can clean your iron on this damp sponge. You just jam the tip into the sponge, or rub it on the sponge. The roughness and water will cause the flux (the brown crud) to wipe off. You can then apply solder to the tip to "tin" it. (That's why you need cellulose, which is wood fiber. A plastic sponge would melt.)
You can also use a damp paper towel for cleaning. It's just not as good.
Clean off the workspace, and if possible, lay a plank of cleaned-off plywood on the table, and solder on that instead of burning your table.
One last thing to get is a multimeter. Digital or analog doesn't matter, but make sure it has a "continuity" setting that will make noise when it senses a short-circuit. You'll use that feature a lot, to test if you soldered things right.
Here's a good tutorial for followup.
http://www.instructables.com/id/How-to-solder/
Now, back to the fixing. You can usually spot a broken solder joint where the connector's pins meet the motherboard. The fix is often just to resolder the broken pin, fixing the connection.
If that's not the problem, look for any cracks along the wire traces or anywhere else. You can bridge the breaks with short bits of wire, stranded copper or sometimes solid copper.
If that's not the issue, then you have to find the broken component. Sometimes, it's a capacitor that's blown up.
That's a bit harder fix, because you have to find the right size and type of cap, or concoct a solution. That's beyond the scope of this beginner article.