I suspect the useful things you can do with this model are quite limited. You need:
* A problem that can be cut into chunks small enough for a low end desktop computer
* One that's solvable without communicating with anything else
* The chunk is solvable enough that the user doesn't interrupt the process
* And the bandwidth usage is small
* And the solution is easily verifiable
* And the problem is big enough that it needs a vast amount of hardware to solve
* But is relatively unimportant, so nobody wants to spend any money to solve it faster
Especially the latter parts seem to mostly suggest quirky uses like SETI. If it's something important you can probably do it faster by just finding funding, than by trying to convince millions of people to install a screensaver.