That stuff looks like the glue manufacturers typically use to hold big caps on to avoid straining the leads.
I'd suspect it's tripping the protection feature, but I find it odd that it doesn't consistently zero the volume. The easy way of testing the output without another pair of speakers is with a dummy load. You can build one or two fairly cheaply. The first thing to check is the DC offset by just putting a volt meter on the output while idling, no source or signal. Ideally it should be zero. If it's more than 25mV you probably have an issue in the output. The next thing to look at would be bias. After that I'd start hunting for leaking caps. And by leaking I mean electrically leaking caps. You're note going to be testing leakage with a DMM though, but leaky caps typically measure above their capacitance rating which you can check with a DMM. Usually you need to remove them to measure them. If it's a blocking cap you should read no voltage across it at idle. Also carefully feel around for unusual heat. Nothing in there should be getting so hot you can't touch it. If you can't touch something for at least 5 seconds it's way too hot.
Another possibility is the volume control itself has an issue. I'm assuming it uses an encoder for the control. The encoder could be going bad, or there may be a power issue in the volume control circuit.
I'm not expert, but I have fixed a few things and built a thing. Hopefully somebody else can tell you more. This stuff is just where I'd start.
I'd suspect it's tripping the protection feature, but I find it odd that it doesn't consistently zero the volume. The easy way of testing the output without another pair of speakers is with a dummy load. You can build one or two fairly cheaply. The first thing to check is the DC offset by just putting a volt meter on the output while idling, no source or signal. Ideally it should be zero. If it's more than 25mV you probably have an issue in the output. The next thing to look at would be bias. After that I'd start hunting for leaking caps. And by leaking I mean electrically leaking caps. You're note going to be testing leakage with a DMM though, but leaky caps typically measure above their capacitance rating which you can check with a DMM. Usually you need to remove them to measure them. If it's a blocking cap you should read no voltage across it at idle. Also carefully feel around for unusual heat. Nothing in there should be getting so hot you can't touch it. If you can't touch something for at least 5 seconds it's way too hot.
Another possibility is the volume control itself has an issue. I'm assuming it uses an encoder for the control. The encoder could be going bad, or there may be a power issue in the volume control circuit.
I'm not expert, but I have fixed a few things and built a thing. Hopefully somebody else can tell you more. This stuff is just where I'd start.