This is a crystal, the central component of a crystal oscillator. There are two main things it could be used for on your MP3 player:
- The main CPU clock, in which case it would be rated for a resonant frequency of several tens of MHz, or
- The real-time clock, in which case it would have a resonant frequency of 32.768 kHz.
Usually, crystals in this type of long, thin package are low-frequency crystals, most commonly the 32.768 kHz I mentioned above. But not always; there are high-frequency crystals available in the same package as well.
If it's just the RTC crystal, you can be certain what frequency it is; I've never seen anything that used any other frequency for the RTC reference. If it's the main clock crystal, you'd need to figure out what frequency the system normally runs at; it's likely that using a significantly different one would cause problems.
The RTC is likely not necessary for the MP3 player to run, but many microcontrollers have the option to also use the low-frequency RTC clock instead of the main clock when operating in a low power mode. That's why I think it could be the RTC crystal causing it not to work; if there's no oscillator, the MCU might go into a low-power mode and then not have any way to wake back up out of that low-power mode, if it works at all. It may even start up in the low-power mode by default.
A few additional notes after reading the comments:
Contrary to my above answer, I would also suspect that this could be a 12.000 MHz crystal, since you note the 1? 000 number and the possibility that it's used for USB. USB does indeed also need a frequency reference, and 12 MHz is standard USB 1.1 full speed.
As for why the crystal could be missing--Years ago, when I was just an electronics hobbyist, I would frequently salvage parts from old devices that either didn't work or were just not needed, since it was easier than ordering them online on a 14-year-old's budget. It's quite possible that someone needed a 12 MHz crystal, found one in an old MP3 player, and pulled it out. I don't know what the history of this particular device is, so I couldn't say how likely that is, but it's a possibility at least.
Crystals very rarely break, though, so if the device was faulty before the crystal came out, it'll likely still be faulty if you put a new crystal in. Still, it'll certainly need a new crystal to work, so figure out the right frequency and stick one in there, then see if it works after that! Since you can tell it's probably 1? 000, there are only so many frequencies it could be, so even trying all possibilities wouldn't be too much trouble if 12 MHz doesn't work.