Macbook Mid 2010 is an LED Backlight screen, it does not contain an inverter. 661-5588 is the Apple part # for the display. If there is a spill inside the machine chances are it could be a problem with the logic board instead of the display. If you connect the machine to an external monitor does it display out to it?
You just need the correct cable for the brand of hard drive you are going to use. I have replaced several of the drives from Apple where they send different brand of drives with the new cable. There is no configuration or anything you need to do just plug in the new cable. What brand of hard drive are you going to use? I can try and find the correct part number for the sensor cable for you.
I have seen this issue with a defective top case before. One thing you can try is to get an external keyboard and mouse. Remove the bottom case of the computer, screws on the bottom of the unit. You can use the following guide here: MacBook Pro 15" Unibody Mid 2010 There is a ribbon cable where the top case/keyboard connector plugs into the logic board. Disconnect that cable. to the left of that you will see a square chip. Right above the chip you will see two silver pads side by side. You can take a flat blade screwdriver and touch the end of the screwdriver with those two. Do not touch any of the other components with the screwdriver. The machine should power on. You will pluge in the external mouse and keyboard. Check and see if the machine shuts down correctly now. 661-5481 is the apple part number for the top case.
Will need some more information, what model of mac is it? Grinding noise is usually a fan or hard drive problem. Some of the newer unibody laptops had a problem with the hard drive cable being faulty and would have strange errors.