the Romans were in fact scared. Very scared. In the end, all they did was starve Syracuse out.
No they didn't. Well, they did for a while, then they did a successful surprise attack during a festival when the walls were unmanned.

A point to bear in mind with modern attempts to test the 'death ray' is that Archimedes understood focus length, knew how to make lenses & concave mirrors & had access to plenty of manpower used to working in teams.
Meanwhile for budgetary reasons most modern teams use flat mirrors with limited manpower resulting in difficulties in achieving a proper focus on the target (& thus lack of ignition)