Here is a Perl related bioinformatics course:
Perl Programming Course for Bioinformatics and Internet
And you can find many more links at:
Bioinformatics.org have a good FAQ.
There is a nice series of 6 or so videos online but I don't remember the link right now. I'll check to see if I have it at home and post it later.

I have both of the O'Reilly bioinformatics books, "Beginning Perl for Bioinformatics" and "Developing Bioinformatics Computer Skills" and may even get around to written reviews one of these days. If you are already an accomplished programer/Perl programer neither will teach you much in that department but they can give you an idea of the sort of biological problems that are out there. "Developing Bioinformatics Computer Skills" gives a good rounded overview of the bioinformatics field with details about common programs. It could be worth your while checking some of the programs out to see the sort of problems people are working on and to find out what field might interest you. "Beginning Perl for Bioinformatics" has some simple but useful scripts that can form a base to your bioinformatics tool kit if you are a beginner or help you think about using Perl with some of the idiosyncrasies of the biological world. As you have more experience you may find BioPerl more your cup of tea.

One of the standard biological books is Molecular Biology of the Cell amazon.com by Bruce Alberts, Dennis Bray (Contributor), Julian Lewis, Martin Raff, ke Roberts, James D. Watson and I highly recommend getting your hands on a copy so that you can figure out what the hell the biologist are talking about. Its clearly written and contains a wealth of basic information.

My background is in Biochemistry although I have since moved to Analytical Chemistry (Biological mass spectrometry) and now use Perl for data munging, automating database searching, and reporting as well as many other tasks. Good luck moving into this exciting field.