bac is correct with the link... The Red X and Red Circle is seen only on the iPod classic. If the suggestions on the website do not help, then this means that the hard drive is faulty and needs to be replaced. I've seen this when working on customers iPods.
Take a look at the top of your logic board by carefully undoing the display cable from the logic board Link text. You do not have to remove the entire display or remove the front panel to see the model number under the cable. If it says, "820-1763-A", this means that this logic board is the first generation iPod video... and meant only for the 30/60GB hard drive models, and it will not support an 80GB. If it says, "820-1975-A", this means that this logic board is the second generation iPod video (5.5)... and can work with the 30, 60 and 80GB iPod video hard drive (maybe even high size hard drives, but I have never tried this theory). Besides it being able to use an 80GB hard drive, it has the Search feature/option on this board. I do not know why iFixit doesn't state this fact. But I made the discovery after repairing many iPod videos and had the same problem.
Try detaching the hard drive from the logic board, then reattach it. Link text When the iPod is starting up, do you hear clicking? This is a sign the hard drive is failing, or has failed. Try restoring the iPod by putting it into Disk Mode: http://support.apple.com/kb/HT1363 If none of those work, then try placing the hard drive in the same iPod model (if one is available) to see if that working iPod sees it... And vice versa. If the hard drive is good, then you can bet it will be the logic board that needs to be replaced. Make sure you replace it with the same model number: 820-1763-A or 820-1975-A.
Try connecting it to a wall charger to see if it forces it to turn on. If successful, it could be the battery. (Even if it starts up, it could still be the following...) If no luck, then it could be the logic board or hard drive... or both.
Same thing happened to mine after it was tossed (by someone else) and hit the headboard of my bed. I can still get audio without headphones, but with headphones-- Nothing. The headphone jack is soldered to the logic board instead of it being a separate piece like earlier iPod models. And so, in order to replace the head phone jack in the iPod touch, you have to replace the entire logic board. Try backing up your iPod with iTunes and then restore it to that back-up copy. If it starts working, it maybe a software issue on the iPod touch. If that does not work, you can always try restoring it as if it is a new iPod, but then you would loose all your data and settings on the iPod... But it is still worth a shot.
First, try restoring the iPod. If that does not solve the problem, then I do not think that it would be the hard drive, it would be the logic board since that is the device that controls how the iPod functions when it is turned on.
First, try restoring the iPod. If that does not work, try opening the iPod to see if there is any damage or corrosion. I have also had it that once I opened the iPod, detached and reattached cables, the problem goes away. If still nothing, try another click wheel. If that still doesn't help, then the final thing it could be is the logic board.