I have a '98 Blazer LT with only 51,000 miles. My wipers started having a mind of their own about 6 months ago...Sometimes they would work, sometimes not. Now they do not work at all. Sometimes I hear a buzzing sound coming from the dashboard area when I turn the wipers to the On position.

Any suggestions on what the problem is and the solution? Thanks in advance for your assistance!

 

Read through this:
Fix for cold solders in the Wiper Motor

And see if that is causing your wiper issues.