Ipod home button is stuck down

It you really really have press down on it that hard to make it sleep than chances are you won't be able to fix it cheap if you are fully up to date you can go to settings, general, then accessibility then scroll down to the bottom and toggle assistive touch on with this enabled you can turn down the volume of your iPod, make it go to home, make it sleep and other stuff

Hold down the power button and the home button.This will "force" turn you're device off.

How to Fix an iPod Touch Stuck in Recovery Mode With a Free Program
An iPod Touch's "Recovery Mode" is for alleviating major operating system issues. Recovery Mode rolls back your iPod's operating system, stripping problematic updates and downloads from the unit. The goal of this total system recovery is to revert the iPod to a stable, usable version. Before you use Recovery Mode, exhaust other troubleshooting methods. In some cases, Recovery Mode is triggered automatically after a failed system update or system restore. When it goes into Recovery Mode automatically, you cannot use your iPod until you complete the recovery process. You can get your iPod Touch out of Recovery Mode using Apple's free iTunes software.

Things You'll Need
-Apple iTunes-USB cable


Instructions
1 Turn on your computer and open iTunes. If you are prompted to download any new iTunes updates, install the updates before proceeding.
2 Plug an iPod USB cable into your computer. Do not plug the other end into your iPod Touch yet.
3 Turn off your iPod Touch. If the iPod Touch is already shut down, skip this step.
4 Press and hold the Home button on your iPod Touch, and plug the other end of the USB cable into your iPod Touch.
5 Release the Home button after you see a white USB icon and the iTunes logo appear on your iPod Touch's screen. At this time, a pop-up should appear on your computer screen, explaining that the software has detected an iPod in Recovery Mode.
6 Click "OK."
7 Click on the iPod Touch from underneath the "Devices" heading on the left-hand side of your screen.
8 Click on the "Home" tab, and then click "Restore." Once it's restored, your iPod Touch goes out of Recovery Mode and you can start using it again. The restoration process takes a few minutes. Do not disconnect your iPod Touch until a prompt appears, letting you know the system restored successfully.

• Press the "Home" and "Sleep/Wake" buttons together for 5 seconds until the Apple logo appears.
• Release the "Sleep/Wake" button but continue holding down the "Home" button. The iPod Touch should reboot, and iTunes will notice the iPod Touch in recovery mode.

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On the iPod touch 1st Gen device, the home button is prone to failure due to the design, most can be fixed for a nominal fee, fixed mine, it was one of the hardest iPods to repair for its time, but with practice, is usually never an issue. Once it is open, then the removal of the battery and then the logic board removal requires experience. As far as the button is concerned, Usually, the "pop" disappears and it feels stuck in the down position, simple fix by introducing an iPod Touch 4th Gen device design upgrade (as far as button is concerned.)
This particular model, the iPod Touch 1st Gen, does not have a replaceable home button module design. It is part of the logic board and so it has to be repaired and not replaced. The small outer disc can be removed and recovered, clean or replaced with another comparable size disc, if the issue is with moisture exposure, corrosion. The sign for moisture exposure issues is that it still "pops" but no longer functions.
I have repaired these successfully and with no issues. www.zfixit.com

Since the sleep/power button is stuck it turned off because holding the top and home button for ten seconds is for turning the iPod off if it freezes so it thought you wanted a hard shut-down and the sleep/power is still being held so it is telling the iPod to turn on but holding the sleep/power button during start-up was made to turn the iPod off if it freezes during start-up. So you may want to take it to your nearest apple store.

Hold down the Power and Home buttons.

If that fails:

Hold down the Power and Home Buttons, once you get the Apple logo, let go of the power button but hold down the home button. Do this when it is connected to the computer it will put it into rescue mode.

Hold power and home to restart it (You might have to hold it for like 30 seconds)  Hold the Home button down as soon as, and for as long as you see the little silver apple. 
After about two minutes if it' still there release, and it'll enter recovery mode, and from there just plug it back in to the computer. You might have to repeat the process about 2 or 3 times, especially if it's jailbroken.  
Also, try holding down the home button while plugging it into the computer. It'll try to bring the ipod into recovery mode as well. 

Try this: turn off your ipod, hold the home button, and plug it into itunes while still holding the home button until the itunes symbol appears with a cable under it. itunes should say "ipod found in restore mode". Restore your ipod to either a backup of that ipod if there is one, or set up a new ipod. (setting up a new ipod will fix any previous problem) (hopefully)