Learn German: Nein, ich habe kein Problem.

The verb changes to match the subject ich (I). For the verb haben (to have), you drop the -en at the end of the dictionary form and add an -e for the ich form, making it habe.

We already said Nein at the beginning. Why do we use kein later instead of just saying Nein again?

Nein is only used to answer a question or state a disagreement, like the English word 'no' at the start of a sentence. The word kein is a negative article used directly before a noun to mean 'not a' or 'zero'. So here, kein Problem literally means 'not a problem'.

Why is it kein Problem without an extra ending like keine?

The ending of kein changes depending on the gender of the noun it is attached to. Problem is a neuter noun (das Problem). For neuter nouns, kein takes no extra ending here. If it were a feminine noun, you would add an -e, like in keine Zeit (no time).

Why is the word Problem capitalized?

In German, every single noun (a person, place, thing, or idea) must be capitalized, no matter where it appears in the sentence. Since a problem is a 'thing' or concept, it always gets a capital P.