Several possible causes from the info you gave
- Battery level low - recharge it for at least 4 hours till the full charge sign displays (2 prong icon instead of lightning icon).
- Time to Reset the iPod - Press the Menu and center Button for about 10 secs till the Apple logo comes ON, then let go of the buttons.
- your hardisk is starting to give problems, hence the skipping and some song refuse to play. - Do a disk diagnostic - follow this post by tt2.
If you have updated any sofware application in Windows, then follow this Apple support procedure
Most likely you have to do all, as the iPod hardisk filesystem would have been corrupted, or else the iPod Reset would bring it to normal operation.