Been a while since I posted here.
I've struggled with welding panels myself. If the plastic is meltable, you can use a clean soldering iron to seal it. Find some place on the panel you can safely cut some plastic off of--there's usually SOME place you can find. Melt the panel and then melt the "solder" into it. Try not to make additional holes. Sadly, just a surface patch weld won't hold. At best it will slow the leak. You have to go deeper which is risky. But there's really no other way. There are plastic welding kits but the cheapest are about $125 to $150. The expensive ones run into the hundreds or thousands. Still, a clean soldering iron can do it.
I have to make one correction: For metal soldering, you NEVER apply the heat to the solder--you heat the part and let it melt the solder. Also, if you are fixing ANYTHING using water that may contact living things (like people) you must use lead-free solder and plumber's flux...I just sweat-soldered in several new cut-off valves for some sinks in my house where the old ones had rotted out, so it's fresh in my mind. I've also done lots of electronics soldering so I'm aware of that kind of rosin-core lead-based soldering as well.
But plastic soldering/welding is much harder. Good Luck!
CarlD