I got lucky with mine. I started having issues with mine around 2000. I lived in Washington, only like an hour from Nintendo of America. At the time, Nintendo still serviced all their old consoles up to and including their current consoles. (This would change in 2006, with the Wii, when they started releasing old games digitally, it was game-over for their long-term servicing of old consoles.) So I took mine in, and if I recall correctly, it was about $50 to get all my games professionally cleaned and for the console to be cleaned, fixed, and sent home with new power supply and controllers.
I wish I had known about that. The cleaning accessories I’ve found over the years have kept it going without issues, but I definitely would have sent mine in for a preventative professional cleaning and refurbishing if they found anything wrong with it.
I remember being a bit surprised when I found out about it, but it also seems to be that a lot of people didn't know about this service, despite it being something Nintendo seemed to pride themselves in for a long time. Maybe they just didn't publicize it widely enough?
I have a hand-me-down NES from a relative that sadly passed away, console works a treat but at some point within the past decade the cartridge batteries went flat. Finally have the gamebit driver to replace them but the gear is all packed away at the back of my storage cupboard...
Could always do the melted pen trick (outside; burning plastic is not good for you). Could risk melting the game cart plastic, though if you get the pen too hot.