Diagnosis loose connection or bad logic board?

My Mac seemed to have had a bad hard drive. It does have a weak battery, but will hold a charge for 10-15minutes. When turned on it would display a folder with a question mark. I replaced hard drive.. worked a few days then started displaying same folder.

A week ago I disassembled and reassembled removing and reinstalling hard drive as well as disconnecting and reconnecting other connections. It worked like a charm until I let the battery go completely dead when in use, the computer shut down of course. When charged and turned on, again failed to boot up and displayed the folder with the question mark. In addition it also when booting up makes a mechanical sound like gears turning??