If it were possible it would likely require that you follow this guide then use a heat gun to melt the glue holding the bezel to the plastic case. Be careful no to melt the case. If that doesn't work it likely isn't possible. There is no iFixit guide for doing it, which tells you something.
When you buy a iMac power supply from iFixit, they send them with a return label so that you can send back your old one for recycling/repair. If you didn't buy the replacement from iFixit, then consider selling it on eBay.
Looks like you found a weekend project! I would suggest you start by clearing off a large table an putting the weed waker on the table and to the best of your ability taking it apart. Take a screwdriver and remove all exterior screws holding on the plastic case, but be careful! Losing a screw can spell terrible news for the weed-whacker. Then hopefuly the solution will be as simple as unwinding the cord form the shaft. If not post more pictures and we can take another look.
To replace the screen on this device, iFixit sells two products: Display Assembly Repair Rated: Moderate LCD Panel Repair Rated: Very Difficult You can save money by only getting the LCD panel but it is a much harder repair. I suggest you mouse through both guides and gauge your own skill. The Assembly includes a new iSight for your machine.
First step would be to unplug/replug and check another appliance in the same power plug. If still having problems try listening closely when attempting to start up. Even though there is no beep it could be starting, listen for the gush of a fan or the spinning of a hard drive. If still nothing it is likely 1 of 2 things: mother board, or power supply. In this iMac I would guess it is the power supply.