On vintage boomboxes, almost all of the plastic parts can be repaired with acrylic solvent cement which fuses the parts as the solvent actually temporarily re-liquifies the plastic allowing fusion. Once dried/cured, the parts should be as strong, or nearly as strong as before the break. However, newer plastics use a different formulation and does not respond to the acrylic or pvc cements like vintage boomboxes. You can typically find these cements from places like tap plastics. Luckily, the solvent resistant forms of plastic is a newer concoction and most boomboxes respond well to this type of repair.
However, that being said, this form of solvent cement repair should be attempted first because in my experience, once other types of adhesives are tried, (such as superglue, jb weld, etc.), they contaminate the surface and reduces the chance of a successful solvent repair. Stripping off the residue can reduce the original plastic making fitment of the joint poor. Remember, solvent cement has no fillers so it needs a good fit.
