Case flexing causes power & WiFi problems

I got a retired Latitude E6400 from work around Christmas. At the time, I thought the only thing wrong with it was a dead hard drive. I had a used 120GB SSD available, so I thought it would be a no-brainer. I bought a docking station, 8GB of RAM, a Win 7 upgrade, and a new Dell battery for it.

Then I discovered that when I tried to actually use it off the docking station, any shift of position would cause the battery to temporarily disconnect and the system to shutdown. Worse, on the occasions where the battery stayed connected, the WiFi would lose connection.

It appears to be a case-flexing problem. My guess is it's because there are some screws missing from the underside of the unit. Does iFixit sell replacement case screws? Or should I try to buy them from Dell?