Changing a business visa to a work visa in Russia?

No, you can't change a business visa to a work visa from within Russia. You'll have to leave the country according to exit date on your business visa, return to your home country, and apply afresh for a work visa. Do realise that these two visas serve incredibly different purposes. A business visa is for foreigners who journey to Russia occassionally to do business, but do not work in Russia or reside in Russia. A work visa is for foreigners who wish to come to Russia to work and live.

Note that work visas are valid for 30 days from the point of entry into Russia. Once you arrive, you'll need to change the nature of the visa from a single-entry visa to a multiple-entry visa, which is valid for one year. Once you have the work visa you can renew it from within Russia.

For more information, read getting a work permit in Russia