It looks like this is another example of multiple inventions required to solve one main problem.
First, shorting would be a problem, but could be overcome with special insulating (flexible) fabrics.
Second, overheating could be overcome by using highly efficient chips that do not generate the kind of heat todays chips do. Finally there are people today making wearable computers using conductive and non conductive threads sewn together to form circuits. If these threads could be miniaturized say down to the molecular level then completely flexible computers could become reality.
Also I was reading an article about nanotubes being used in logic gates the other day. If this could be done practically then I believe that everything from flash memory (the obvious replacement for hard drives) to flexible screens could be created and folded up without any damage. Just don't drop them in the paper shredder!
If computer networks become advanced enough then most items like hard drives and optical drives (CD/DVD's) would not be required as they could have access to these items by locating them and accessing via a server on a network, much in the same way that the small computers you sometimes see in librarys that essentially keep all software and hardware on the server and access it via a network connection.
Looks like you have a great idea, that will no doubt become reality someday!