Difficult, just from text, but it reads to me like the “no FX” is what you’re hearing and the “on” is broken up somewhere in the chain. Could be very simple (something unsoldered) or a burnt-out or a dud. I’m on holiday imminently, but a photo of the internals would help.

As for a compressor, I can only speak for bass. I bought an Ibanez BP10 yonks ago because my bass at the time had a really uneven response across the strings. Not such a necessary now that even cheap instruments have bearable pups, but it does have other uses. The “attack” knob can make the most hamfisted plec sound like fingerpads of cotton wool, but it’s easier just to vary technique (on a bass – guitar is perhaps trickier). The sustain knob can’t be replaced by technique; that thing used to keep a note going through a cig break if required. I haven’t used it in literally decades but, if the idea appeals, that’s what it does.