I'm typing this on a Dell D600!
Usually lap tops are 3.5v active high? I will have to measure mine.
But it should be possible to connect a 2N7000 gate to the P.P. output and switch the SSR with the output of the 2n7000.
Ideally the power for the switching could come from the D600 power adaptor, 19vdc, or another DC source.
If more than a few have to be switched then a ULN2805 could be used.
Search 2n7000 here for a circuit example.
Desk top would be better, but even then, a buffer as above is ideal.