No, not necessarily But you will need some combination of experience and/or certification in the area of technology that you want to get work in.
Do you want to work with computers, networks, servers, hardware, software (etc). Each area is specialized and each area requires a specialized area of technical knowledge.
Probably the easiest way to 'break in' to the field is by becoming a Microsoft Certified Desktop Professional. You can get this certification by attending a week-long course, do some self study, and then go take the MS Desktop Professional Certification exam. Then, once you get the entry level job you can branch out from there. Some people absolutely loath Microsoft, but the simple fact is that almost 90 percent of the office desktops are some sort of MS flavor. If you find you don't like doing desktop troubleshooting, you can branch out into networking, security, system admin, web , database - I think you get my drift.
As for experience, how do you get it (because no one will hire you without it - and how do you get it if no one will hire you)? You have to get it, by 'paying your dues'. This most often means working as a volunteer IT person at a non-profit organization like the Red Cross or your local church or VFW club, or whatever. Or you can work for menial wages as a intern for an IT firm. Both ways of getting experience really suck, in my opinion, but there is no other alternative that I see.
So there you have it. You don't need a computer science degree, necessarily, but you DO need a combination of certifications and work experience. No one I know will hire you for a decent IT position (at a decent wage anyway) without a combination of both certs and experience.
Hope this helps.