#1
My Fender Jazz 24 is distorted, and I don't know why. None of the controls do anything to affect the distortion, and turning the volume down doesn't clean it up either. I replaced the battery and nothing changed.

I'm playing through my POD HD500X through my Presonus monitors. I have no issues whatsoever with my Ibanezes (SR300F & SR800).
Spin 'round carousel when your horse isn't screwed in.

My band:
Fractured Instinct
(For fans of Death/Groove/Prog Metal)

Ibanez RGA42E
Ibanez S420
LTD H-301
Ibanez RG520
Peavey Predator USA
Douglas Grendel 725
Line 6 Pod HD500X
#2
is it your ibanez active? could be the output clipping the preamp of your pod since you said the bass has a battery
...it was bright as the sun, but with ten times the heat
#3
If replacing the battery did not help (and I am assuming you did not accidentally replace a dead battery with another dead battery - it does happen, you know), then you have a wiring problem; almost certainly with (a.) the wires leading from the battery to the EQ pots, or (b.) the wires leading to the bass output jack. Take a look at them and see if any are loose or even not at all connected. It should be an easy fix.
"Maybe this world is another planet's hell?" - Aldous Huxley
#4
The Jazz 24 and the SR300F are active, the SR800 is passive.

I'll check the connections, but it's really daunting. All of the pots and the preamp are jammed in the cavity, and it is just a colossal cluster**** of wiring. I don't like dealing with preamps in a bass.
Spin 'round carousel when your horse isn't screwed in.

My band:
Fractured Instinct
(For fans of Death/Groove/Prog Metal)

Ibanez RGA42E
Ibanez S420
LTD H-301
Ibanez RG520
Peavey Predator USA
Douglas Grendel 725
Line 6 Pod HD500X
#5
I have limited electrical experience. The most I would do is inspect the wires, jiggle them around a bit and see if that helps. If not, then it's going to a pro.
...it was bright as the sun, but with ten times the heat
#6
I've sprayed contact cleaner in the pots and the jack, and it seems to have helped a lot.

I'm thinking that maybe the Fender's pups are just way hotter than the pups in my Ibanezes and my POD patches have to be adjusted for the Fender.
Spin 'round carousel when your horse isn't screwed in.

My band:
Fractured Instinct
(For fans of Death/Groove/Prog Metal)

Ibanez RGA42E
Ibanez S420
LTD H-301
Ibanez RG520
Peavey Predator USA
Douglas Grendel 725
Line 6 Pod HD500X