2nd gen iPod Touch with a faulty screen, home button, or both? I have an 2nd gen iPod Touch which has something wrong with it. The screen does not work unless I hold both the Sleep and Home button for a few seconds. The screen then lights up as normal and I could access all the apps whilst holding the Home button (Sleep button released). 

However, when I release the home button, the screen blanks out again. But the iPod still functions normally, I still can listen to music, connect it onto the laptop and even skip to the next song by touching the part of the screen where the arrow button would be if the screen was illuminated. I could hook the iPod up to a sound system and it works just fine. It even charges normally when connected to a power source. 

Does this sound more like a screen problem or a home button fault or something else?
It sounds like you have a bad front panel.

The front panel of the iPod touch (screen cover, touch sensor and home button) is a single piece with a ribbon cable connecting it to the rest of the iPod.

If you are at all handy changing the screen cover &amp; home button is not that difficult. You can get the parts and tools you need from iFixIt for about $75 with Shipping.

There is a video demonstrating the removal of the front panel.

When I cracked the screen on my 3rd gen iPod touch, Apple was going to charge me half of the iPod's new price to replace it. Since I didn't really care if I completely trashed it I decided to go this route. The surgery was successful and the iPod works perfectly.