What can I use to build a live video recording, streaming, marking application / platform?
Check out Wowza - it should do what you want. The basic premise of Wowza is video in, video out. It can take multiple video streams into it's encoding engine, and spit them out in various formats, live.

If you've got 4 inputs (let's assume they're cameras with HDMI output), you need a computer with 4x HDMI input cards (or 2x computers with 2x cards, whatever), that then sends the 4x streams to a Wowza server, then the Wowza server can either be directly accessed by viewers, or pushed out to a cloud service (like Amazon S3 or EC2 for example) for viewing without bandwidth constraints.

Using Wowza will get you a live stream of your event without using a service like Livestream/UStream. 

I'm not 100% sure on marking clips though. Using Wowza gives you the flexibility to use your own player, so if you wanted to add markers within the video timeline, that users can click on and see that specific moment in the video (even during a live broadcast), that would be how you'd do it. But how you'd get the player to read some sort of file for the markers, and how you'd publish the marker information to the player, is beyond me. It might just be easier to create a "highlights package" for people to view later, that's just a YouTube video of clips you've edited together from the live footage.