Why isn't my charger working? (LONG)?

I have a 4th generation iPod Touch, updated to version 5.1.1. I bought a bundle of chargers, with an iPhone charger just so happening to be in there.
There's no problem with it - other than the fact that it sucks.
About 2 days ago, it stopped working. It just didn't work. I have to hold it in a specific position for it to charge when it dies; and that isn't even the worst part.
It won't charge when it restarts. Even if the wire is in the EXACT position it was when it was able to charge.
When it loses all of the battery, it only charges just enough battery to restart. Only like, 10%. Even though it says, "20% battery remaining", it only dies like 5 minutes later.
Let's break this down:
20% dies in 5 minutes.
20 divided by 5 is 4.
That means that 4% of battery is supposedly drained every minute.
That's 1% every 15 seconds!
That's insane!
Why can't it charge like that!
Moving on, sometimes, it actually is 20% charged, and lasts me a little longer. I have a special app (called Battery Pro) which tells me how much battery I have and how long it lasts if I do something.
For example:
Listening to music: 6 hours in sleep mode.
Surfing the web: 1 1/2 hours.
What does it really say for surfing the web?
2 hours.
2 hours.
2 HOURS.
I'm lucky if I can get 2 minutes out of this battery, but 2 HOURS! Really! At 20%?
Well, I know what you're thinking:
"Why can't you just get another charger?"
Well, first off, I know. It's cliche.
Second, I got in a car accident on Tuesday. I don't have a car. And the nearest Walmart (or any places that sell phone accessories) are miles away. I can't walk there, (obviously) and I can't afford to get a taxi to go All the way out of town for a lousy charger.
So that only leaves one option: the Internet. More specifically, eBay. It's cliche, too.
I'm lucky enough if the battery can stay long enough for me to find and purchase one.
Will that even work?
Why isn't it working? Is it my iPod, or just the charger itself?

It sounds to me as though you have a combination of problems here.

Problem #1: You most likely have a broken wire inside the insulation on the charger. This is why you have to fiddle with the position to get it to charge at all. This DOES NOT explain the quickly dieing battery.

Problem #2: You, like most people, use and depend on your electronics. So what happens is that after a long day you are getting ready to leave for some fun on the town. You notice your phone / tablet / laptop is run done and you have to leave soon. You plug it in while you hit the shower and get dressed then disconnect it and leave with it. Not a problem, right? Wrong! Most rechargeable batteries on the market, Li-Ion, NiCad, NiMH, etc require long, full charges to work properly long term. They all loose the ability to hold a charge properly if recharged in short bursts of electricity. They have a name for this: battery memory effect. The substances inside chemically change when they release their charge. When they are recharged properly, they reverse the chemical process. When recharged for short periods, not all the chemicals get reversed, so they hold less charge. Unfortunately, if these chemicals aren't reactivated soon, they loose the ability we prize them for, the ability to release electricity in a useful form. I believe this is the problem with the battery time you're getting.

There's a fix you can try. Run the battery absolutely dead by leaving the phone on, then put it on to charge for at least 24 hours. Repeat the process until the battery gives you better / acceptable charge times. Or buy a new battery. Remember to charge in long periods, don't plug and run!