Our remote control for our Jensen JE2608 is not responding - we have replaced the batteries but still nothing - it seems the little light does not come on - do i need to replace the remote??

Normally, when the light does not come on and nothing happens, it means that there's a fault connection inside the remote somewhere critical (Meaning a wire is not touching where its supposed to.)

My brother fixed several remotes, but he's an electronic whiz and used a good deal of soldering.
Give the remote a few good taps (smack it on your hand, never hit hard surfaces), and see if it makes its connection again, even for a moment.

Whether or not this is the problem, it sounds like you'll be needing a new remote. I suggest going to walmart or best buy and talking to an employee about remotes and which ones work for which televisions, and then order one for a decent price online.

Sidenote: Make sure that the batteries are in correctly.
Make sure that the springs in the battery compartment are functioning as they should and the batteries aren't sliding around, even a little.

That's all I got. Hope it helps.