Using your personal laptop for work is unheard of for anything other than a startup that is still a couple dudes in their basement. (Where you are one of the original dudes)
Run away.
Run away.
Just to conform, and in case I needed a working machine until I found out whether they were serious enough to properly supply the necessities.
If not, then I could carry on with my own "good as new" laptop dedicated to the employer as long as necessary until I had collected enough pay to get an additional one for myself. Nicer one too.
Before even thinking about making any waves.
Using your machine "until I found out whether they were serious enough to properly supply the necessities." makes no sense whatsoever. They aren't. You don't need to waste any energy finding out, they fact that they asked gave you your answer.