The court in London heard that student Christopher Weatherhead, 22, was studying at Northampton University when he purportedly took part in a distributed denial of service (DDoS) campaign against PayPal.
It was said that Weatherhead was part of the Anonymous hacking group, which targeted companies who opposed internet piracy, but who later attacked PayPal after it refused to process Wikileaks payments.
Weatherhead denies a charge of conspiracy. He has pleaded not guilty to conspiring to impair the operation of computers between 1 August 2010 and 22 January 2011. Three other men have already pleaded guilty to the charge.
As well as PayPal, MasterCard, Visa, the Ministry of Sound, the British Recorded Music Industry and the International Federation of the Phonographic Industry were also targeted by the Anonymous group.
Prosecutor Sandip Patel said PayPal was chosen after it refused in December 2010 to process payments for the Wau Holland Foundation, which was raising money to keep Wikileaks going.
Weatherhead is said to have used the online name Nerdo, when posting plans for the attacks on an internet relay chat (IRC) channel hosted in Russia.
Patel said PayPal was the victim of a series of attacks "which caused considerable damage to its reputation and loss of trade".
He said more than 100 workers from PayPal's parent company eBay spent three weeks working on issues related to the attacks. PayPal, it was heard, also had to pay for more software and hardware to defend against similar attacks in the future. Patel said the total cost to the firm was "estimated at £3.5 million".
The prosecution said the BPI, which was the subject of an attack in September 2010, had paid out £3,996 for improved online security, whilst the Ministry of Sound had spent an extra £9,000 on security after its four websites were attacked in October 2010.
Weatherhead's home had been raided on 27 January 2011, where computer equipment was seized. The trial is continuing.