Clint is on to something, and I must agree with him. The fact that it works with the lid off is a huge clue. It suggests to the RF-savvy that the antenna, or the transmission line connection between the receiver and antenna is bad, such that the transmission line (coax, board traces, etc) inside the box from ant to input is picking up the signal, not the antenna. When the lid is put on, the line acting as an antenna is now inside an RF shield (or at least inside a wave guide below cut-off frequency of FM which is 87-108 MHz), so no signal. This is what I'm thinking. It is probably quickest to try another antenna first.
"Alive without breath, as cold as death; never thirsty, ever drinking, all in mail never clinking."