Learn Hardcore Icelandic: Ég kaupi tölvu.

At the start of a sentence, Icelandic capitalizes the first word, so ég becomes Ég. The word itself is the same pronoun (I); capitalization is just normal sentence formatting.

What does the accent in Ég do? Is it a different letter?

Yes—é is considered a distinct vowel in Icelandic (not just an optional accent). It affects pronunciation and can distinguish words. In Ég, the é is pronounced roughly like yeh/yeah (often described as a ye sound), so Ég is approximately yeh(g), with a light g sound at the end.

Why is the verb kaupi and not kaupa?

kaupa is the infinitive (to buy). kaupi is the present-tense form used with ég (1st person singular):

ég kaupi = I buy / I am buying
Other present forms include:
þú kaupir (you buy)
hann/hún/það kaupir (he/she/it buys)
við kaupum (we buy)
þið kaupið (you plural buy)
þeir/þær/þau kaupa (they buy)

Does mean or ?