The earlier (Middle English) form of the first person pronoun was ich, pronounced like the modern English word "itch" (compare modern German ich). Another form ic or ik was found in the North of England.

It was this northern form from which the final consonant was dropped to give the modern I.

As for the spelling, there's no clearly accepted explanation for the capitalization. The Oxford English Dictionary (first edition) writes only:

The ME [Middle English] ic, ik, were also spelt yk, ych ..., also with y, Y, and finally with the introduction of printing settled down as I.

The earliest citations given by the OED for capital I or Y (other than at the beginning of a sentence) is from Wyclif's New Testament translation (late 14th century):

And anoon, Jhesus spac to hem, sayinge, Haue ȝe trust, I am