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Pocket BASIC??????

Help! I am way into BASIC. Lately, I have been wanting to make a little DIY pocket computer with a basic gray scale screen and nav buttons that can run simple  BASIC programs uploaded from my computer. I looked around Google to find somewhere to start, and found out that no one has ever attempted building such a thing before. One site suggested that I should look at mobile motherboards by TI and Atmel. However, when I arrived at the websites, I found a bunch of complex, expensive boards that have unnecessary fetures such as WiFi and touch. I need some help on what hardware configuration to use (aka mobile motherboard, chip set). Help!

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One of the best ways to get into microcontrolers when you are familiar with Basic is to use the BX-24, or Basic Stamp.
They are pretty easy to program, and the company has some experimenter/prototyping board that make the hardware part pretty simple. There are lots of add-on hardware pieces available as well.
Go to www.parallax.com to take a look at what's available. I've used them for some very simple projects as well as advanced robotics.
PKM5 years ago
Graphing calculator! At school I had a Sharp EL-9600 (amazon link) which I had great fun programming BASIC programs on.  The one I had is showing its age now with limited RAM and a slow processor, but I could still write an orbit simulator, a bunch of mathematical and statistics programs, and a simple game a bit like Worms.  They are great as cheap portable devices with a screen and keyboard that you can write programs on.

I agree it's a shame there is no device like the one you describe, but building one from scratch will be a massive task.  The only vaguely approachable angle I can think of is a microcontroller (AVR?) running a BASIC interpreter, perhaps loading programs from an SD card, and connected to a cellphone LCD as a display.
Err. I used to have at least two computers, from Sharp, dating back over 25 years that were pretty similar to what you want, except they didn't have multi-line displays.

If you really wanted to do something with a working on board BASIC, I suggest you look at the old 8052AH-BASIC chip, in its latest re-incarnation in the P89V51RD2, done by http://www.efton.sk.

Steve