I realize it sounds preposterously ambitious for a startup to try to become as big as Apple. But no more ambitious than it was for Apple to become as big as Apple, and they did it.
I thought about this before, and I think building a hardware startup like Apple, or a systems software company like Microsoft is an order of magnitude harder than when they were founded. Let us take Apple. When Apple was founded, there was an ocean of people that did not have a PC in their homes. Big, uncharted market. When you hear Don Valentine (Apple's investor from Seqoia) talk about it, you can see how they did not care about anything but the market. Do we have that kind of market today? Maybe. At the moment everyone is occupied with their ipads, phones, and PCs.
Technology. Today the hardware is so complex, that it can be only competed with by largest companies in the world. It is not a coincidence that it is only Samsung that can compete with Apple in mobile devices. Take a Texas Instruments or Qualcomm chipset, you will face a complexity barrier at every corner. We won't hear you saying things like, my co-founder designed a chip so efficient, it will be a game changer. Anyone remember the JoJo Pad before the ipad was released?
So what could be done? I think it comes down to playing on the above two variables. For a new hardware/systems startup, it must target uncharted territory, i.e. introduce (mobile) computers to an area of use where it has never been tried before, and make sure everyone in the world needs it. (Like that thermometer startup, except find a wider use case) Use existing cutting edge technology, and build your new technology upon them (e.g. I would probably start with a top notch chipset + android + add new, hard-to-replicate technology.)