I'll go with the super glue suggestion also. Depending upon the type of plastic, a specialized plastic glue, specifically the plastic glue made to build plastic model airplane kits may be a good choice. Also check out Eastwood, they sell plastic "welding" kits.
Oh...for buying things like super glue. Go to a store that sells supplies for high end radio control model airplane enthusiasts. This store will be selling to modelers who spend several thousand on their model airplanes, helicopters. These stores will have the specialized super glues, putties, tools, etc that will really help repairing your plastic car interior parts. They sell a selection of super glue in various strengths and various set up times. For instance one super glue product is sticky but doesn't set up. It's sticky enough to hold things in place, and later move around, but doesn't harden. When everything is correct, you paint over an accelerator and it immediately hardens. They also may have putties that harded when you shine an ultra violet light on the putty. The stuff they sell won't be found in a neighborhood hardware store.
Also, when gluing plastic parts, I try to cover the surfaces I don't want to glue with masking tape. I inevitably get the glue on my fingers and then without masking tape, I've left plastic glue finger prints on the other surfaces. I use masking tape to prevent "finger prints" and overflow onto finished surfaces.
Can we hear how successful you are in your glueing project? Thanks
If it weren't for my vettes, I'd be in the RC model airplane hobby. In Torrance, my home town, about a month ago, I turned into a residential street to find a rather large F16 model airplane taxi-ing towards me. I stopped and could see a man about 100 foot away with an RC transmitter. Anyhow, the model F16 made a U turn and I followed it down the street. and stopped next to the man with the transmitter unit. I asked about how it was powered. It was making a rrrrrr-ing sound and didn't sound like a piston powered ducted fan. He said it was a TURBOJET! I looked at it and could see the heat waves coming out of the tail and I pulled up right along side it and then I smelled the kerosene. This was a big bucks model airplane, not only a turbo jet, but also, it had nose wheel steering! Damn, so many fun things in life to play with and not enough money/time to enjoy!