Try recording with Audacity. It will show the signal amplitude as it's recorded. Your waveform should exceed 80-90% of the size of the window in the loudest passages. If you aren't able to get the amplitude high enough then make sure you're adjusting the volume in the *recording* section of the volume control panel and not the *playback* section.
Other than that, allthumbs battery suggestion is your best bet. Most A/E have a higher output than electric guitars because they have a battery powered preamp. But even if yours isn't preamped it still should be louder than what you describe.
What's interesting though is that you say that you get a lot of noise when you up the volume. Is it hum or crackling? Maybe your cable is bad.
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