Researchers estimated 50,000 years of computing research would be needed for the bid but it will instead be completed in just one year through the "world community grid," IBM said in Bangalore, where it has a research facility.
Volunteers will donate their unused computer time for the research by registering on www.worldcommunitygrid.org and installing a free software programme in their computers.
When the PCs are idle, they will seek data from the world community grid, perform computations using it and send the results back to the main server. A screen saver will tell individuals when their computers are being used.
Calculations will then be performed to find the best combinations of drug molecules that will inhibit the replication of the viruses that cause dengue, West Nile encephalitis, yellow fever and Hepatitis C, IBM said.
Once these are identified, researchers can begin testing these drugs to determine their effectiveness.
"Viral diseases such as dengue continue to be a serious health concern around the world because there are no known drugs to effectively treat them," said Maharaj Kishan Bhan, a secretary in India's department of biotechnology.
"Continued research and global collaboration is needed so that scientists can better understand these viruses and then develop treatments that could save many lives," Bhan said in a statement released in Bangalore, southern India.
Dengue fever is found primarily in Asia, including India, while the West Nile virus affects Africa, Asia and Europe and has now moved into the United States.
Both have no known drug treatments, are primarily passed to adults and children by infected mosquitoes, and are responsible for millions of illnesses, as well as thousands of deaths each year.
In India, dengue fever has affected more than 46,000 children and adults between 2001 and 2006 of which almost 700 were fatal.