Currently all government agencies have a vast array of personal computers. Typically government employees only use a portion of the computing power of these computers in their official duties. The untapped processing time of computers represents a vast untapped resource to the government.
The software exists to take large complex computations typically handled by supercomputers and parse out small parts of these computations to individual personal computers. These personal computers use their idle processing time to compute the data and send it back to a central location where it is assembled back into its desired state. When multiplied across the entirety of government computers, this network would represent an enormous chunk of computing potential.
This process could be completely transparent to the user and be configured to not overtax their processors. This has already been used widely in the private sector by asking private citizens to voluntarily install community grid software on their computers, mainly for charitable/research work. (http://www.worldcommunitygrid.org/)
The government could use this process to make its own complex computations, realize a revenue stream by allowing private companies to pay a fee to use the government network for their computational needs, or could simply use it to benefit non-profits, educational foundations or charitable organizations for the benefit of society at large. It represents a large benefit the government could easily realize through little or no upfront investment of its own.