With no computer background, you've got a long way to go to get to where you want and need to be. I'd suggest that you start out by working on the CompTIA A+ and Network+ certifications -- you need not necessary get these credentials, but you will want to learn the material involved to make sure you're ready to deal with even elementary infosec (information security) topics, tools, concepts and so forth.
After that, I suggest you visit www.informit.com and search for "tittel security bookshelf" (omit the quotes) from the home page. This will turn up a two-part bibliography of the very best books on infosec topics. Start with the Dieter Gollman and Kaufman/Perlman/Speciner books and begin working your way systematically through that bibliography.
Once you've got three or four of those books under your belt, you can start thinking about an introductory infosec certification. I recommend the CompTIA Security+ as a good place to start. After that you'll be pretty well able to follow your interests and the market without my help.
Total cost for A+, Network+, Security+: about $625 for exams and another $450 for books and practice exams. That's not a terrible cost to have to bear over the 12-18 months it will probably take you to complete this work ($1075 over 12 months is about $90 a month; over 18 months about $60/mo).
Good luck and best wishes! You'll have to put in some serious time and effort to reach your goals, but you can do it. As for the whole "employer funding of certifications" issue, reports from Certification magazine do indicate that funding is down 20% or more over last year, but in your case I suspect the lack of support dervies more from the possibility that you are asking for IT training support when it may be likely that you're not even working in IT at present (how else could you have no computer background?).
For more information on this topic, visit these other SearchSecurity.com resources:
Ask the Expert: First certification for breaking into security
Ask the Expert: How long does it take to get up to speed on security?
Ask the Expert: Suggested reading for infosec novice
This was first published in December 2002