iPod 4G Monochrome — Replacement Headphone Jack (Thin - 20GB)

Yes. Try known-good headphones first. Sound still in one ear only points to the headphone jack. Crackling points to the headphone jack, then the logic board.

Very low volume with every setting turned up, on more than one pair of headphones, most likely points to a worn jack, then the logic board — there is no Volume Limit setting to check on this model (Apple's 2004 guide lists its whole Settings menu and there is no volume cap on it). Clean the jack opening, check the headphone/hold ribbon seating, and try a known-good plug before ordering.

Yes: on every model the Hold switch is part of the headphone jack assembly, so a broken or stuck Hold switch is fixed by a new assembly. On the 4th Gen and iPod Photo an iPod stuck on Hold (locked whatever the switch says) is the headphone jack cable first — often just not pushed fully back in after the case was opened: push it back in — then this assembly. This thin assembly is not interchangeable with the other case thickness.

Match the assembly to the case thickness before using audio or Hold symptoms to choose a part: this is the thin-case assembly (20GB). The capacity engraved on the rear panel tells you (40GB = thick, 20GB = thin), and the bodies differ by hand — Apple lists the 20GB at 0.57 in deep and 5.6 oz, the 40GB at 0.69 in deep and 6.2 oz. The assembly mounts to the rear panel, so match the back that is actually fitted. Check variant fit before replacing another audio or input part.

Apple's 'Classic' branding started with the 6th Generation (2007). This is the iPod 4th Generation (Click Wheel), the monochrome-screen model from 2004. Apple's official name for this model is iPod (Click Wheel).