Bicycle Mechanics - front bike wheel shimmy

On a road bike (10-yr old Trek something or other, carbon frame), does anyone know what may cause the front wheel to shimmy when the front brake is applied? I have cleaned the rim really well, switched the back break pads up front, and made sure the front wheel is on straight. None of that worked. Is it the frame, the wheel or the brake components? Any ideas? Thanks for your help.

The rim is sectioned to gether opposite the valve hole. Sometimes that join will cause a thump as it passes through the brakes. You might try turning the wheel around to reduce it or sanding down the raised lip, if the join has a misalignment.
You could also have a misadjusted headset. To loose and you would get shuddering under braking. To tight might give speed wobble.

Can you describe the shimmy in a little more detail....

At what speeds do you notice it?
Is it a side-to-side shimmy or front-to-back studder?
Is it present when you brake soft and hard?

Thanks for your insights. More info: the shimmy is side to side. It occurs when the brake is pressed hard, the harder the brake, the more noticible the shimmy. So, it's noticed when trying to brake hard from higher speeds.

I'll look at the rim when I get home. Also, the headset - that's where I thought the trouble may be - maybe the headset is somehow crooked? But, I'm pretty novice at cycling and maintenance.

Check to make sure the front wheel is true. In other words, when looking at the wheel as it spins between the brake blocks does it move side-to-side (aka. wobble)?

Shimmy is usually a term applied to resonance in the bike frame that occurs when the wheels turn at a certain speed. If you have a frame which suffers from shimmy, its really just bad luck. Some frames are more resistant than others, but Ive never seen any serious work on how to design a frame which does not suffer shimmy.
You brake-induced troubles sound like something else, probably a bump or warp in the rim. Rotate the wheels slowly, and gently apply the brakes. See if the rim catches at any point.
You can check the headset for tightness, stand by the bike and apply the brakes and rock the bike back and forward using the handlebars. If there is any loseness, you will feel it.

Standing above the front wheel, grab the wheel . Try to wiggle it side to side. If there is any movement at all, you need to tighten up the cone.

Next, grab the fork with one hand and the handle bar with the other. Try to move it against the frame (headtube). You are looking for movement in your headset. If there is play you need to tighten your headsest.

Thanks so much for your replies. I'm going to investigate further this evening. I will check back after that. Many, many thanks!!!

Good advise above. Also, make sure that the fork is secured into the headset.

Sometimes, the headset gets loose. You really notice it when you apply the brakes.

To test, apply the front brake and push your bike forward. Can you see any play in the headset? Do the handlebars rock forward a little? If yes, this is a very bad situation. If you aren't sure how to tighten your headset, go to a pro.

Sounds like the headset to me...Give mike's instructions a go.