<< Has anyone here went into computer science without any programming experience? >>
I did just that. Well, I had taken one programming class in high school but it was extremely simple and many years before. In my first year of university, many people I came to know taking Computer Science had little or no prior experience. Not all stuck it through, but many did finish the program and graduate. I actually found that some people with previous experience were sloppy programmers (didn't write or think out their code ahead of time, poor comments and readability in their code), not that they weren't very bright.
The CS program at my university introduced topics in the first year such as basic theory and programming principles which included: writing structured modular code, readability, re-useability, basic to more complex data types, algorithms, recursion, and abstraction. It assumed no prior knowledge (so I think you should be fine knowing only HTML), but did, of course, assume logical thinking by the student, and a strong mathematical foundation (my school has a Mathematics Faculty, math did not play second fiddle). After the 'introduction', things quickly took off into more abstract concepts and theory in second year. The assignments got very long and much more difficult.
Believe it or not, C/C++ was never formally introduced; students had the choice of which language to use for assignments by the third year.
As far as my particular experience, I switched programs after two years. I guess I lost interest, but don't let me dissuade you ;}, as I mentioned, others I knew (who had no experience upon entering the program) went right to the end.
If you persevere, you will do fine. As far as the job market goes for CS graduates, the word plentiful comes to mind. If your school has a Co-Op program (alternating work and school terms), I advise taking it. The work experience and contacts you build up is invaluable. I regret not utilizing this resource. If you have any more questions about computer science, let me know.
Regards,
Al