I'm as skeptical about vaccines as you are, but, let's be clear, not everyone who eats fish which contains Mercury becomes ill.
It depends on what you class 'an illness'. If you age quicker, are far more likely to get cancer and heart disease, and are far slower mentally, does that class as a disease?
As for the HPV/cancer connection or lack of one, I was unable to pin down an appropriate website on the internet. However if you think about it it had to be a shockingly embarrassing virus that caused cancer rather than the measles or the common cold.