Circular saw doesn’t cut properly

Back in the day when I used to put up vinyl siding, I found that the best way to cut it with a circular saw was with a cheap 140 tooth plywood blade installed backwards (to give the teeth a negative rake and prevent chipping):

For really hard plastics, I've used a diamond abrasive blade before and that did a great job (these are incredibly expensive if we're talking about a single cut though). I would imagine an abrasive blade for cutting metal would do just as well though:

You should be able to pick up either of these for less than $5.

Wear good safety glasses and do a trial cut first with whatever option you go with - plastic will chip long before it will bind the blade in most cases, and these can be both sharp and high velocity.

Honestly, a 12 year old black and decker probably needs to go to the scrap yard. Low end saws are not built to be rebuildable, at least since the late 20th century (some 50 year old "low end" saws were a lot less "low end" in construction) - a 21st century low-end saw was usually built with "planned obsolescence" from the design phase forward.

Provide the exact model of your saw to check some details.

The one thing (if that's been left serviceable on this model) it might be worth trying is to replace the brushes if they are excessively worn. Beyond that, replacing the saw is far more likely to be cost-effective.