Dusty sensor/inner lens! How can I clean it?

Sorry, this isn't a Canon P&S, but since I'm here so often and I get so much help with deciding on a DSLR and lenses, I figured it's worth a try.

My "backup" camera is a Panasonic DMC-FX01. Over the course of three months of having it, dust has made its way either onto the sensor or inside of the lens. I'm positive these imperfections are not on the outer part of the lens where I can easily clean them off.

I can only see them at full, 3.6x zoom. They're manified when I place my fingers on the outer edges of the picture, to give it contrast, since I can't set anything manual on this camera. I've attached a picture of what they look like.

Is there ANY way to get this off? I tried blowing compressed air in the seams on the sides of the lens, and in the battery compartment(>_> to no avail. I sometimes have bigger pieces of dust stuck wherever this is, and i can...uhh...slam the camera against something and it goes away. That's not safe, and it also doesn't work for these pieces.

Again, sorry it's not about a Canon camera, but I figured I could get some general advice on what to do. Thanks a lot.

The large dark areas are my fingers, since they appear best when there's contrast, but the circled areas are where dust is currently. Sometimes they appear bigger than others, and are noticeable in real world pictures.

Anything I can do?

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How old is the camera? Is it worth taking to a photo shop and seeing about a repair or professional cleaning?

Unless the lens is intended to be removed, you're better off getting a repair facility to tackle it.

It's only four months old... -__-

I'm reluctant to have to do something like that since it's new-ish. I'll look into it, though. Unless it's worth trying to take apart.

If it's only 4 months old, send it back to the manufacturer for warranty service. Dust spots will show up easiest at small apertures and long focal lengths.