A red x is a sign of a hard drive problem. Do not worry though;
Try this link http://support.apple.com/kb/TS1463
Also, some people (including myself) report that if you hit the iPod it works again. Take the iPod, make sure that it is charged, make sure the bottom of the iPod (the dock connector) is at the bottom when you're holding it and just hit it a couple of times on your open palm. If that doesn't work try hitting a bit harder. If hitting hard on your hand isn't working try hitting it, in the same way (dock connector at the bottom) hit it on a table.
If all this isn't working you may have to replace the hard drive. You have the choice of giving it to Apple for repair, ask a local repair shop to do it or do it yourself. The Classic has a 1.8" hard drive. Here is a link to a repair guide: http://www.ifixit.com/Guide/iPod+Classic+Hard+Drive+Replacement/564