My P200 has a mark on one of the inner lenses. An example of the smudge marks is here (above the green house). The smudge appears in every photo in the same spot. I did some stuff on my own, but the smudge remains. Is there anything else I can do?
That linked PDF looks thorough, and pretty cool!
If you followed the instructions, and you managed to clean the glass elements accessible to you, the next step is to disassemble the zoom lens assembly and clean the elements inside.
Whether this is possible, or even if it's a good idea, is up to you.
The P200 looks like a nice camera, but it was introduced 6 years ago according to DPreview. Unfortunately many compact point-and-shoots are built for economy, not robustness. You may have to conclude that trying to fix this issue isn't worth it.
I have the same camera, with a similar problem and yes it is old but still great as when I bought it.
When you go to a tropical country, typified by high heat and humidity and having air conditioning indoors, moisture can condense in your lense. This causes fungus to grow in between multiple lesnses, places which you can't access to clean without dissasembling the lense. It is stringy and appears like dark fuzzy worms that are most visible when you are zoomed in to enlarge.
I had an old Nikon lense disassembled and cleaned years ago at high cost. The reason I found this post is to ask whether it is affordable to clean the inside of a Sony Lense.
Most lenses were multiple if they have zoom capability. So, the only way to avoid this is to have a bag of dessicant and store your camera in a vapor proof bag with the dessicant in it, when you enter your air conditioned hotel room. Even then the dessicant bag might become so moisture saturated that you need to pan fry it, or put it in a microwave. That is hard to do in an inexpensive hotel room that doesn't have these conveniences.
And if your camera lense starts acting dumb, rather than retracting or extending fully, it is the battery.