Orange Memorial Hospital is now known as Orlando Regional Medical Center. They most likely have those records archieved and you may be able to request a copy through them. See link below.
You may be able to have better results by going through the vital records of live birth with the State of Florida. But, it would be necessary to get the exact date of birth through narrowing down the time by your hospital stay. The sex of the baby will also be necessary.
Shyla RN
http://www.orlandoregional.org/ormc/
Also, if you have ever checked out adoption.org or reunite.com it could help you with Florida law and help your search along the way.
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