I've had this problem too. For me, the reset didn't work, but cleaning the jack solved the problem. I didn't have to open the Ipod to do what I did - it's a non-invasive procedure, won't hurt anything.
In many devices, the input jack where you plug in your headphones is called a switching jack. There are metal contacts inside that normally touch each other, completing the connection that makes the internal speaker play. Plug in your headphones, and those contacts open, disabling the internal speaker.
These type of contacts get dirty or corroded over time, and can act intermittently or fail.
Frankly, I'm not sure if this device uses this type of jack - usually the symptom is that the internal speaker won't come back on when you unplug the phones from this type of jack, because the contacts aren't making clean contact. This is the opposite problem - the speaker stays on when you plug in headphones. The headphones may be sensed electronically in the Ipod, but this still requires solid electric contact between the jack and the headphone plug. Anyway, the following cleaning worked for me when a reset didn't:
Dip your headphone's plug into some rubbing alcohol and insert and remove it from the jack several times. You might try sucking on the input jack, or blowing some compressed air from a can in there (available at a computer store). You might try these techniques several times. The canned air is also good for drying out the jack after alcoholing it.
The other thing is to frequently wipe off your headphone plug before you insert it in the jack. Hand oils can make for poor electrical contact and dirt buildup on the jack contacts over time.
DON'T spray electronics cleaners or WD-40 in the jack - some of this stuff has solvents that can destroy certain plastics.
It's not a bad idea to do this every few months as protective maintenance. It takes 10 seconds.