What could be wrong with my laptop charger or my charger input?

I have an HP Dv7 Entertainment just like this one. Recently, I’ve been having issues with it charging and I can’t tell if it’s the charger or the charger input on the laptop itself.

I first noticed the issue when my laptop’s battery randomly died on me even though it was plugged in. The battery icon on my toolbar will tell me that my laptop is “plugged in, charging” for hours while the charger is plugged in, but every now and then it will change to the regular battery meter as though I unplugged the charger. The light beside the charger input that indicates the laptop is charging will also be off when this happens. I’ll remove the charger from the laptop and put it back in but the light won’t come back on and my laptop won’t say “charging.” If I wiggle it around and turn it slowly in the socket, it will eventually start charging again.

The cord near the input plug head is worn out, but the charger box gets warm, so I don’t think it’s the charger itself losing power or anything, though I’m not ruling that out. If it turns out to be something wrong with my input socket itself, what can I do to fix it? Could I do it myself? If not, where should I go and how much should I expect to pay? If it is the socket, why does it work when I wiggle it around sometimes?

Also, my battery is getting to the point where it doesn’t hold a charge for as long anymore, if that has anything to do with this which I doubt, but you never know.

Thanks in advance.