I just fixed mine and my wife's ashtrays. They each had different issues. Both seem to be the only common issues that you can have. Mine would not shut all the way due to the spring breaking free from the plastic, and falling behind the tray. Hers would not stay closed and just spring back out when pressed in. It is pretty easy to get the ashtrays out, if you just follow the instructions that were provided. The hardest part for me was getting the cigarette lighter out of the old ashtray housing to put it in the new. You have to use something like a small screw driver or a knife as I did to get the green plastic part to release from around the metal portion of the lighter. There is also a connection that does not seem to be connected by the factory that I went on and hooked up so that the light works around the lighter.
From what I've found, you should be able to get the inner ashtray holder out of the housing without removing the entire thing if your goal is to simply remove the broken spring so that you can close the ash tray all the way. Here's how, remove the actual ash tray by simply pulling while it is in the open position. Now you are left with the inner portion that slides in and out. There are tabs on both sides of the slide rails that engage tabs on the housing. If you use a screw driver to pry the housing slightly away from the rails, then the tabs will disengage and that side will pull out slightly further. Now do the same on the other side, and the entire part will come all the way out.
By doing this, I was able to use a new ashtray assembly to fix my wife's, and combine her good housing w/ spring intact and my sliding portion with a good catch tab to make a working tray for mine as well.
I hope this doesn't come off too confusing to read, let me know if you'd like anything clarified.