So the dust cap is gone and the leads were cut?
Looked up what the "Solokon" cone is made out of--Kicker does not really say but it is injection molded so that leads me to say plastic. I am going worse case scenario and would guess something along the lines of the polypropylene family of hard to glue slick plastics.
Call up your local Lowes or Home Depot and ask for Loctite Epoxy Plastic Bonder. It is made for slick plastics and should hold a new dust cap. Follow the instructions on the twin tube exactly and apply a very light coat to a new dust cap.
Here is a link to the bonder
Loctite Epoxy Plastic Bonder from Loctite Adhesives
For a new cap, try to find a thick plastic that "feels" like the plastic of the cone. Scuff the glue side with sand paper so the glue can get some grip. Stuff a paper towel in the hole of the cone and apply a thin coating on the cone. Remove the paper towel and let the glue get tacky. Use a piece of plastic that is close to what the cone is, your choice of what color to use. Apply a very thin coating to the plastic plate and let the glue get tacky. Once both the cone and the plastic glue has become very sticky and the epoxy won't move, lay it on the cone and throw some weight on it until it cures.
If you use too much epoxy, it will fall into the voice coil and trash the sub.
If you don't trust yourself to not get the glue into the voice coil, find somebody that has some experience working with epoxy. Youtube might have some videos about it for an example.
Soldered the leads? Uhhh, OK--whatever works! If you want to get a better hold, find an old speaker laying around and rip the leads out. Lay a 1/4 inch of old lead across the break and solder it in place.
Hope it works out well for you
