You can go from Rio to Foz (see the falls) which will take around 25 hrs. Then get a bus from there to Corumba (Brasil border) via Campo Grande. I think this is another 20 or so hr journey. Then you can cross to Puerta Suarez on the Bolivian border. From there you can get a train to Santa Cruz which is an overnight run and from S Cruz its possible to get a bus to La Paz which you can also take overnight...
I dont know about 7 days though...You might find yourself sitting on buses and trains most of the time...
If you are stuck for time you can get a flight from Peurto Suarez/Santa Cruz to La Paz which costs only aorund 60 dollars with TAM which is the military airlines...
I did a similar journey but I spend a night in P.S. and a few nights in S Cruz...
hope this helps