Computability

To start, let me first admit ignorance in the realms of complexity, incompleteness, etc.  I have not yet taken those classes and am still at the popular science level.

Can any computer compute any problem?  If not, what makes a universal Turing machine special in that regard?
On a similar note, could, say, my 1995 Pac Bell computer run modern applications (architectural differences aside) given enough time?  Or are there other constraints in place, such as more RAM needs that could be lifted for the sake of argument to make that computer capable?

This is a purely academic curiosity.

modern/non modern computers are capable of solving anything that is explainable/convertable in math numerical methods within a certain amount of time depending on the machines capabilites