The correct way to fix this problem really would be to order a new case, or shop the internet for a non working notebook of the same model and switch the cases out. however not everyone has the money to do this, or is really worried about the job being nice and neat when they are done. In this case it was a school laptop that needed to be fixed ASAP, and the customer didn't really have money to invest in a new case or spare parts. So I proposed a cheaper solution that would work just as well and cost pennies on the dollar. The only down side is a few cosmetic changes.
For this project you will need.
1. (6) #4-40 x 3/4" bolts with nuts.
3. Power drill with a 1/16 bit
4. Needlepoint Pliers
Step 1: Drill Your New Holes
Use the bit to drill all the way through the case where the screws would normally go. You may have to remove the metal tabs that the screw is supposed to thread into. If the chassis is cracked they are useless anyway.
Use compressed air to remove any debris from drilling.
Next, put your monitor back in place and run your bolts through the holes. You may have to lightly thread the bolts through the plastic. Use this to your advantage and go slow, do not try to over tighten using just the case plastic. Thread them down just far enough that the bolt sticks through the other side of the case.
Step 2: Secure Your Bolts
If the bolt and nut are not snug simply dab a little bit of lock-tight on the nut so it wont back out. If you followed instructions so far the bolt shouldn't wiggle because it's threaded through the plastic. If you managed to strip the hole though simply pack the underside of the old screw chassis with a bit of Bondo or some resin, in a pinch you could put some Lock-Tight in there, but if you ever have to take the monitor off later you are going to run into some problems.
Step 3: Sometimes There's a Third Screw...
Note: One of the screws did have a pice that set above a speaker. I didn't want to risk hitting that with the drill so I slightly dog eared the path of the bolt. It's slightly off center, but doesn't look any worse than the other one.
When I was done I simply stuck some of those felt feet that go on furniture on the bottom to keep the bolts from scratching a table up.
Other than the bolts on the bottom, and the two screws now neatly placed by the speaker grills above the keyboard. Everything works just fine, lid opens and closes without any issues, and the customer was happy.
Total work time was about an hour of labor and a quick trip to the supplier to get the right size bolts.