Making a Functional Computer out of an Arduino Uno
The keyboard can be done simply using a PS/2 keyboard - it's just serial, and there's plenty of tutorials out there for it.

Storing data can be done simply on an SD card - there is a shield out there already to do that.

As for the video - that's considerably harder.  If you want the Arduino to generate a PAL video signal for instance then you have your work cut out for you.  Yes, it is possible, and someone has created an Arduino "pong" game, but it's very chunky graphics and only black and white.

For VGA you will require some form of interface to do the work for you.  Sparkfun used to sell the Picaso video card that could be made to work with the Arduino, but alas that has been discontinued and there are no plans as yet for a replacement.

TBH your best bet would be to use something like a Wyse terminal and communicate with the Arduino completely using serial.  Much simpler than messing with video signals and such.