Hardware hacking: No, it's not illegal. (Except for modchips. Shhhh). Hardware hacking is taking apart a piece of hardware and improving it. This hobby takes many forms. You can Circuit bend, modchip (shh!), and my favourite: Portablizing.
Can you see what that is? It's a PS2. It's handheld. It runs on batteries. Impressive. It's things like this that have made Benjamin Heckeldorn internet famous. It has also landed him a nice payroll.
This kind of thing isn't really hard. Just find the necessary voltage and amperage, solder on a battery that meets the requirements, hook a screen to the video out port, and slap a case on it.
Confused? This probably isn't for you then. Just learn some amateur electronics, get some supplies and try out your great new hobby!