Is your check engine light flashing or on solid? If its flashing that's a sign that it's misfiring and you probably need new plugs and possibly coils. If it is on solid and not flashing I would get the codes read and see what it is saying and could be many different things.
Try connecting it to a computer and see if it is recognized by your computer. If it is recognized without actually looking at your phone I would think that the screen went bad. You can generally find out if your backlight is bad by taking a flashlight and placing it on top of your screen to try and illuminate the lcd. If you can see an image then your backlight is bad and you would probably need to have your screen replaced.
Check out youtube and see how others are repairing it. Sometimes you just have to clean the board and it may work or as Dan above said you may have to replace components. If that is the case you need to learn how to test components and be able to replace them. A decent soldering station is a must along with good testing gear and a lot of patience. A schematic/layout isn't completely necessary but it does help and usually will make testing much quicker.
Use a multimeter and with your powersupply plugged in but disconnected from the wii carefully check the voltage from the end of the cord you would plug into your wii you should see 12v DC or a little bit above 12v.
Try taking your battery out and removing the bios battery from the board (not using anything metal lol) also make sure the power cable isn't connected either. Once you have this done press the power button a couple times holding it in for about five seconds roughly. Put the batteries back in plug your power cord in and try turning it on. This may or may not work but what it should hopefully do is remove all power from the capacitors and computer it self and if there was protection built into the chip hopefully it should cause the chip the shutdown and reset. No promises that this will work but once in a while it does help. Let us know what happens.