I've got a problem with my Nikon D5100 that I bought in 2012/2013. It's either the camera itself, the battery or the battery charger.
I don't know anyone with my set of equipment and can't really test whether it's because of the battery, charger, or camera. Therefore I want to know whether there are other means of how to check if the fault lies in one of them (or all of them) and how to solve it without spending money for another camera.
It used to work fine. I shot a fair amount of pics and (mostly) recorded videos of around 5 minutes each. Then I didn't use it for a few months. Yesterday I wanted to use it again. Charge it. Put it into the camera. And now it doesn't work anymore. The green light in the battery folder is lightning up when I put it in. And there is also a sign that the battery doesn't have lots of energy anymore - even though I charge it the whole night.The display doesn't go on. Needless to say I can't take any pictures with it. I never used flash or anything like that.
I've read a lot of posts that the battery of the D5100 is the culprit. Therefore I'm currently tending to buy a new battery (this time not from Nikon again but from a 3rdd party) or a grip. I've also read though that 3rd party batteries don't work in the newer D5100 (meaning cameras bought in around 2013) anymore?
From the description you've supplied it looks like your battery has failed and needs replacing. The easiest way to test it is to find someone who has another d5100 near you and try your battery in their charger / camera. The d5100 is a very popular body and it is likely that someone you know has one (or another camera that uses the same battery.)
Li-ion cells tend to be an area where you get what you pay for. 'Compatible' batteries are often less powerful and/or have had corners cut in production. Where they are equivalent in power and production they tend to be a broadly similar price to genuine Nikon batteries.
Unlike a lot of other battery types Li-ion cells contain a flammable electrolyte solution consisting of lithium salts in organic solvents such as ethylene carbonate and ethyl methyl carbonate. That means that when poorly made (or even well made ones in the case of faulty batches) Li-ion cells carry a fire or even explosive risk when not made properly (Source: Chemical and Engineering News: Assessing The Safety Of Lithium-Ion Batteries).