Let's try to disassemble all that. We'll ignore the ampjack for now; just the Rumble. One should always plug instruments and leads into amps with the volume down to zero. I'll assume that's what you'll be doing from now on. OK then, volume at zero, lead plugged into the Casady, the other end plugged into the amp (to be done in that order. Turn the volume up on the Casady. Now turn the volume up slowly on the amp. Does the bass play..? If so, all is well. If there's an increasing 'buzz', but no sound from the Casady pick-ups, there's a faulty jack socket on the Casady which needs fixing. Fairly simple for those with some soldering experience, an inexpensive operation for an instrument repair shop (recommended, unless already familiar with these things...).
As for the Ibanez, the same experiment should be executed, in the same order. If the guitar can be heard, all is well. If there is a buzz, it's the same problem as the Casady. If the guitar plays, but only very, very quietly, it's, again, a job for a repair shop, and could be a number of things (you've already eliminated the possibility of a low battery, so it's not that...).
Try all this and report back, please..?