What is the ruling on affiliate marketing for an online computer company, which involves receiving a commission when a new user registers or when a purchase is completed?

Promoting permissible companies is allowed. This is done by bringing customers in exchange for a known commission for each customer or for each sale completed through you. This falls under the category of brokerage (samsarah) and recompense (ja'alah), as evidenced by the Almighty's saying: "And for he who brings it is the burden of a camel, and I am [responsible] for it" (Yusuf: 72). Your ignorance of what the company takes from advertisers does not affect the transaction, as the determining factor is the agreement with you.