Is a PDA as powerful as a CPU?
If you count a CPU (as you imply in your text) as an unbounded memory and the processor, then no you can't model it as a PDA. A push down automaton (with one stack) can only recognize context-free languages, for example $\{a^n b^n c^n | n \geq 0\}$ cannot be recognized by a PDA, but presumably could be recognized by your blue computer with massive graphics card and DVD.

Typically, we think of your blue computer with massive graphics cards and DVD as a Turing Machine, because that often proves to be the best way to model it.

On the other hand, if you model your CPU without unbounded memory, then PDA is still not the right model. If your CPU has no memory or only a small (i.e. bounded) amount of on-chip memory, then it can only be in a finite number of states, and is better modeled as a DFA.