Have you ever tried letterbomb hack to mod the wii and to read games off the external hard drive. I used to do this a lot back in the day the modding stuff and pretty easy on the wii there's also videos on YouTube to help you do this.
It's very easy to replace the gears and common sense once you open the drive you will see they pull right off and the new ones slide right back on and make sure you align them up and but the tray in and test it before closing everything up to make sure everything good if so put it together and go on with playing.
Hi have you opened the console and cleaned it and replaced the thermo pasted sounds like it's overheating or the power supply is overheating. Try the console cleaning and try powering it on and listen to the power supply box and see if you can hear the fan spinning in the power supply if you can't the fan it's not working or clogged with dust and causing it to make the power supply to overheat after awhile and shut down.