Can I file that patent?
Query answer is subjective in nature, You have to check if combination of known elements yields more than just predictable results. In other words if your solution to new problem was achieveable by prior art.
As per MPEP:2143 Examples of Basic Requirements of a Prima Facie Case of Obviousness
Exemplary rationales that may support a conclusion of obviousness
(A) Combining prior art elements according to known methods to yield
(E) “Obvious to try” – choosing from a finite
number of identified, predictable solutions, with a reasonable
expectation of success;
For more information you can visit MPEP
Do I need to arrive to an agreement with the owners?
Again this question is subjective in nature, If product patent claims all components and there is no way to design around it you require a license to use it. In case you can exclude any component then you need not require a license for said claim. However there are many other ways to protect product e.g. method of making, using, arrangements, design patents etc.