Check the voltage regulator in the back of the alternator. Check the light bulb in the instrument panel, if it's burned out, there is no power to the rotor coils and no voltage is produced. You check it by turning the key to 'on' and looking for the lighted alternator indicator.
This is a good site for repairs, by a Volvo Master Service technician.
http://volvospeed.com/maintence.htm
Also, check the battery cables for corrosion. Clean the battery connections.
How old is the current battery?