My Mac won't Shut Down and is running Slow

Question

It began with my Mac not shutting down or restarting.  The shutdown process will end with a white screan and the thinking icon in the center. 
Slowly, over a few weeks, the comuter began running slowly.  Now my apps seem to be freezing on me often.  iPhoto, Aperature, & Light Room have all frozen on me at some point.  Other programs run slow. 
Do I have a hardware problem?
A Virus? 
thanks in advance for your help. 
Jason
Model Name:          iMac
  Model Identifier:          iMac11,3
  Processor Name:          Intel Core i3
  Processor Speed:          3.2 GHz
  Number of Processors:          1
  Total Number of Cores:          2
  L2 Cache (per Core):          256 KB
  L3 Cache:          4 MB
  Memory:          4 GB
  Processor Interconnect Speed:          5.86 GT/s
  Boot ROM Version:          IM112.0057.B01
  SMC Version (system):          1.59f2
  Serial Number (system):          W8****B6
<Edited by Host>

Answer 1

First question is how much free disk space do you have?  Generally, around 10%+ is needed for OS X usage.
While you may not have spinning beach balls, see these two FAQs for things to check:
http://www.thexlab.com/faqs/sbbod.html
http://www.thexlab.com/faqs/performance.html