Is it legal to record gameplay of games?
absolutely not lots of people record gameplay
How can you record gameplay from an Xbox 360 or PlayStation 3 using a s-video cable that plugs into a computer?
Online gameplay is free in most cases for PC, though some games may require subscriptions to play online. The most notable sorts of these games are the MMOs, such as EVE Online and, most famously, World of Warcraft. In general though, most online gameplay is free in both the case of retail games and internet browser games.
To record you Xbox 360 gameplay, you will have to purchase a capture card. You plug the component cables of the 360 into the cap card and then plug another set of wires from the cap card to your TV. If you have a wired cap card, it plugs into the computer and the software will record it. If you have a wireless cap card it wirelessly connects to your computer and records that way.
You could use free screen capture software like LiteCam or HyperCam. But to use these you'll most likely also need the Dolphin emulator to play your Wii games. Luckily the LiteCam program allows to record with built in Web Cams or externals so you can still use it for free and record on your TV instead.
It's very possible you don't have enough space on your hard drive to record more then 4 mins. or You have the settings set to only record 4 minutes of gameplay before shutting off. or You should maybe try and update to the latest drivers and see if that helps. Also make sure you have it installed correctly if it's a computer part rather then a PVR.