Hello Sano344,
Thank you for the details of the issue you are experiencing and the troubleshooting steps you have already taken. It sounds like you are seeing a screen similar to this when trying to adjust the volume using the volume keys:

I recommend the following steps for an issue like this (you can skip any of the steps you have already taken):
- Verify that the volume is set to a level you would normally be able to hear.
- Ensure that there is nothing plugged in to the headset jack or the dock connector.
- If the iPhone is in a protective case, make sure that the speaker port isn't blocked by the case.
- Make sure that the speaker and dock port aren't clogged with debris. If necessary, clean it with a clean, small, dry, soft-bristled brush. Carefully and gently brush away any debris.
- If an audio issue occurs when using a specific application, try testing other applications to see if the issue persists.
- If the iPhone is paired with a Bluetooth headset or car kit:
- Restart the iPhone.
- If restarting doesn't fix the issue, ensure that your iPhone is updated to the latest version of iOS.
- If the issue is not resolved after restoring the iPhone software, please contact Apple Support.
You can find the full article here:
iPhone: No sound or distorted sound from speaker
http://support.apple.com/kb/ts5180
Thank you for using Apple Support Communities.
Best,
Sheila M.