I am trying to find a replacement part that goes on a PCB of an LED C size battery-driven hanging lantern light. One of the two leads of the small barrel shaped component corroded and broke off near the surface. Can anyone be of any help in providing what I can use to replace the barrel? There is no stamping of any kind, it just a metallic small barrel with two leads soldered to the PCB.
That's most likely a crystal, there's probably a micro-controller under one of those black epoxy spots and the crystal is used as it's timebase.
Crystals in that package style are commonly 32.768 kHz, which is a power of 2, so easily divided down to 1 Second for real time clocks (they're often listed under the name "clock crystal"), but they can be other frequencies.
Others are saying it could be a tilt switch as there are some of those in a similar package. If it is one something should happen when the lantern is turned sideways or upside down such as the light going out (not sure why they would do that, it's not like a kerosene lantern that could catch fire if you knock it over). If it did have some functionality related to tipping it over that would indicate a tilt switch. The power switch has a 4 hour and 8 hour setting, which would mean it has to keep track of time somehow and a clock circuit using a crystal seems reasonable. Even without the need for accurate timing microprocessors need a timebase, and a crystal is one way to get one.