Quite simple to detect: remove all expansions, hdd, accelerator etc., keep only the motherboard as it was manufactured. Then switch it on and look at the power LED. If it goes on and half a second later becomes brighter, the board is ok. If it stays dimmed, it is damaged. Check processor, Kickstart-ROM, Chip-RAM and CIA chips.
In order to connect an Amiga to a VGA monitor you need a
scandoubler. You should rather get an
Amiga to SCART cable and connect it to the TV this way.
Bye,
Thomas