iPod Classic will not respond to any button pressing.

Time for some unconventional action then.

Try these things, in the following order:

1. As you already have a low battery warning, I suggest that you unplug the iPod from power and let the battery run down completely. In other words, leave it alone for 24 hours.
2. Only once the iPod has completely run out of power, plug into power to re-charge it. It can take up to thirty minutes after plugging it in before you see any response from the iPod. Even then, leave it alone for a few hours. When you re-check it (after a few hours), has it started correctly? Can you get any response from it? If you can, leave the iPod until it's fully charged. If it now works correctly, good. If not, try the next step.
3. Once the iPod has been charged, try a Reset. Turn the Hold button on, then off again and then press-and-hold the Menu and Select (centre) buttons together for at least ten seconds. The iPod should restart. If it continues to behave in the same way, that suggests to me that the iPod has failed.
4. If you have got to this point and the iPod is still doing the same thing (cycling between "support" and "low battery", that suggests to me that the iPod has a hardware failure.

If you have tried a Reset, as mentioned above, and that hasn't worked, then connect it to your computer and see if your iTunes can see it. If it can, then use iTunes to Restore the iPod. Restore is a separate procedure to a Reset.

Otherwise, as I mentioned previously, perhaps the iPod has a hardware failure, in which case you may need to see if you can get it repaired or simply buy a replacement.