Laptop only charges when 100% battery?

My 4 year old Toshiba L500D -00X will not keep its charge unless it's already at 100%. The only way I can charge it is if I close the laptop and leave it be until fully charged. I had it in to be fixed a few months ago and the man who supposedly fixed it replaced both the charger and the battery, which I had replaced on my own a month prior. I haven't gotten it wet, I haven't dropped it, I haven't bent the cord, the fan is fine… I have no idea what is wrong with my laptop.
Usually I don't have to worry about my laptop randomly losing its charge unless the cord is out for too long and it becomes 99% charged, but my sister and I recently bought Minecraft and whenever I play it for longer than 5 minutes it says its plugged in, not charging and I have to shut off my laptop until it's fully charged again. This really gets on my nerves because I like spending time playing Minecraft with my sister.

Also, in case anyone says the problem is that it's just old and running out of life, I bought it brand new and didn't start using it until 2 years ago because my screen wasn't working, so while it's 4 years old I've only been using it for half its life.

I really hope someone can tell me what's wrong. I can't afford another laptop and this one holds a lot of sentimental value for me.

It's not because you're not using a battery that it's not getting bad. Actually, if you're not using your battery, it's worse than whether you're using it and taking proper care of it.
The current type batteries that they use in computers, seriously degrade when the charge becomes less than 10%. If your computer has been sitting still doing nothing for 2 years, it will have degraded tremendously. I've had the same thing with a mobile phone that I didn't use for 7 or 8 months. Barely used it and I'm not getting an hour of idling out of it anymore.

Get yourself a new battery mate. You can get pretty cheap ones on ebay… Just make sure you buy the exact model you have now.