plastic piece that holds window in place

Thanks for posting. That housing is part of an assembly called a Coil Balance system. Within that block there is a coil spring that indeed helps regulate the opening and closing of the window. If the coil springs have snapped, then you will have to replace them. 

Now, I'm afraid that label on the sash tells us nothing about what kind of coil balance you're working with; but fortunately I think I have an idea from the shape of the housing. Usually the spring connects to a plastic block further down the window track called a pivot shoe. The pivot shoe is connected to the bottom corners of the window sash (the part of the window that actually has glass and slides up and down). The best way to identify what coil balances you have is to see the pivot shoe. I suspect it looks like something like our 15-192. If so, what I actually recommend you consider doing is replacing this entire assembly with our 15-259 Pivot Shoe, as well as the Series 159 Coil Balances. The video below details everything you need to know to attempt this. Take a look and let me know if you have any further questions. 

I'm sorry to say that the exact part isn't made anymore. The suggestions made above remain our best and only options for you: either trying to adapt the 15-192 Certainteed brand part to work on this window, or totally converting the entire assembly as per the video instructions.

As for replacing on both sides, it's always wise to do that. You never want to mix old and new balances, otherwise the new springs will wear out very quickly from overcompensating for their weaker partner.