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Your question "how to get a display out of the frame of a consumer product" doesn't have anything to do with electronics. For the same reason as asking how to get a shelf out of your fridge has nothing to do with cooking.

Regarding troubleshooting actual electronics, here's from an answer I wrote at Electrical Engineering to someone who wondered if they could ask similar repair questions:

- Is this some manner of high/mains voltage device? Repairing such electronics is very dangerous if you don't know what you are doing. In particular, unplugging the power cord doesn't mean that the device is now safe.
- Do you have the necessary tools for trouble-shooting? In this case the minimum is a multi-meter, a soldering iron, some tweezers and/or flat nose pliers depending on component size. Preferably also an oscilloscope.
- Do you know how to use the above tools with some confidence? In particular, if you are repairing a surface-mount board (which is the most likely case), do you have experience soldering such boards?
- Do you have basic ESD awareness? Consumer electronics PCBs are often easy to break with ESD.

This is the bare minimum before you should even consider repairing this project by yourself. If you are uncertain about what some of the above even means, you should leave repairs to professionals and your question would definitely be off-topic at the EE site too. 

It _can_ be on-topic but then you must be able to trouble-shoot this at some extent by yourself, drawing up simplified schematics, measuring voltages, read out what IC there are and track down the datasheets for them etc. That is, you need to know basic electronics.