Learn Hardcore Japanese: pasokon no syuuridai wo kaisya ga haratte kuremasita. - The company paid for the computer repair cost.

The particle の is the genitive (possessive) marker. It links two nouns to show ownership or association. Here, パソコンの修理代 literally means “the repair cost of the computer.”

Why is 修理代 marked with を?

修理代 is the direct object of the verb 払う (“to pay”). The particle を marks the thing that is being paid.

Why is 会社 marked with が, not は or に?

が marks 会社 as the subject (agent) that performed the action of paying.
Using は (会社は) would topicalize “the company” and might imply contrast or a broader topic.
Using に (会社に) would make it an indirect object or recipient (“to the company”), which changes the meaning.

What does くれる add to 払ってくれました?

くれる indicates that the subject performs an action as a favor for the speaker (or someone in the speaker’s in-group).
The structure ～てくれる emphasizes that someone did something beneficial for you.
So 会社が払ってくれました means “The company kindly paid (for me).”

How is 払ってくれました different from 払いました?

払いました is a neutral past statement: “(Someone) paid.”
払ってくれました conveys that the payment was done as a favor to the speaker and often implies gratitude.

Could I use もらいました or あげました instead of くれました?

もらいました (“received”) shifts the focus to the speaker as the beneficiary. Example:
私は会社から修理代を払ってもらいました。
This highlights “I received the favor of having my repair cost paid by the company.”
あげました (“gave”) wouldn’t work here, because the company is the giver, not the speaker.

Why is the verb in the past tense くれました? Can I say くれる?

The past tense くれました indicates the action has already been completed.
You could use non-past くれる in a general or habitual context (e.g., “The company usually pays…”).
For a specific completed event, past tense is the appropriate choice.