Number one fatality for remote controls is the ceramic resonator that is used to produce the 38khz carrier frequency. Cheap to replace. Often they are placed on the PCB in such a way that if the remote is dropped the resontaor will "slap" into the PCB, destroying the resontor. When I replaced them, I always glued them down.
As Someone Electro said, check for broken solder joints also, especially the IR LED.
Another common problem is dry joints on the 'large' decoupling capacitor, and as already said, dry joints on the IR LED, and broken ceramic resonators. Incidently, while the IR modulation is about 38KHz, it's derived from a ceramic resonator about 455KHz.
I think, other than loose connections, u could have broken components, not just the resonator, but anything else: maybe the chip it another stuff when it disconnected from the PCB...
The thing you are talking about is proboby a transistor.
Its a boxy yellow plastic or metal rounded thingy that has 2 (a crystal) or 3 (a resonator) pins.
If you throw an pentium in the flor you will break its fragile pins.If you throw an DIP chip in the flor you will only bend its pins (you can bend them back)
Check for lose conections.You may want to take it to someone who knows electronics stuff and has the tools.
The part with the number 455 on it is a ceramic resonator, 455 Khz. You can get one from another remote, or even some AM portable radios, to test if it is OK.
Basically the material they are made from!, a ceramic resonator uses ceramic, and a crystal uses a slice of quartz - quartz is a GREAT deal better than ceramic, it's far more stable and accurate - so if accuracy is required you would use a crystal. If accuracy isn't too important, a cheaper ceramic resonator would be sufficient - most micro-controller project would be perfectly OK with a ceramic resonator!.