Could someone list places around the Chattanooga/Cleveland, Tennessee
area that train for the CompTIA A+ core and OS exams and Network+
exams (the shorter the duration of the course the better). Please list
web addresses, phone numbers, and possible prices for courses. Also if
you could list some online training couses that would help also.

This site of CDI has training locations.  You can call them to check
on the Chattanooga(listed there) or Cleveland areas.
If you wish to check out other trainings sites, using www.google.com
enter the terms "A, Network training" +Chattanooga +Cleveland"  The
sites listed by this search should get you all the training companies
and their locations.

http://www.netwind.com/html/locations.html