Need help with fixing vintage DT990

[Enolaa]

Hello, I have owned a DT990 from I believe 1987 for a couple years now, and lately it has caused me issues. I hear a lot of static in the left ear, and the cable feels finnicky, dropping sound depending on if I'm touching it or not, as well as its position.
I opened it up, and this is what it looks like. I have tried unsoldering the wires but they are surprisingly uncooperative, and my best efforts haven't been able to desolder them. I would love to get some advice, as I am a complete newbie and frankly quite bad at DIY.
Thanks in advance.

 

[GREQ]

First let the soldering iron heat up as high as it will go. So let it cook for a couple of minutes before using it.
Then add a small blob of solder to the end of the iron tip before trying to melt the connection.
The extra solder should help it to melt faster.

 

[Enolaa]

First let the soldering iron heat up as high as it will go. So let it cook for a couple of minutes before using it.
Then add a small blob of solder to the end of the iron tip before trying to melt the connection.
The extra solder should help it to melt faster.

That's pretty much what I tried, but it seems like the solder really didn't want to melt..
Thanks for the pointer though, will try again later!