Good questions, Clare.
If you have never worked with electronics, I wouldn't recommend starting with a TV. They're sometimes unforgiving, and can be dangerous.
Here's what to do next... you need to know that this TV was designed with a self-diagnosis feature. There's a little microprocessor inside the TV that monitors for abnormalities, and signals us through that flashing LED when it senses a problem. The circuit is designed to flash the LED in a certain pattern to help us determine where the problem could be.
Well in this case, 7 flashes on a TX-P42VT30B, indicates a failure of one of the TV's sustain boards
. These are the boards responsible for sending signals to the plasma panel (the screen). They work pretty hard, and failure regularly I'm afraid.
You should bring the TV to a local repairer. Alternatively, if it's too awkward or heavy for you to move, they might come to you.
I hope this answers your question. If you need any clarification, fire away. If you're good to go, please don't log off without rating my service. I hope it was excellent!