Which is correct?

J'ai besoin de l'Internet et un gomme.
J'ai besoin du Internet et d'un gomme.
J'ai besoin de Internet et un gomme.

What do you mean by "un gomme?"

An eraser.

I thought so -- but it didn't seem to go with internet.

This is the correct sentence.

J'ai besoin du Internet et d'une gomme.

Note that gomme is feminine

The correct sentence would be "J'ai besoin d'Internet et d'une gomme." Let me explain why:

In French, when expressing the need for something, we use the phrase "avoir besoin de" (to need). After this phrase, we need to use "de" or "d'" followed by the noun.

In this case, the noun "Internet" begins with a vowel sound, so we use "d'" instead of "de". Similarly, the noun "gomme" begins with a consonant sound, so we use "d'une" (d' + une) to indicate "a eraser".

Therefore, the correct sentence would be "J'ai besoin d'Internet et d'une gomme."