I've a lot of experience in HTML5, JavaScript, ASP.NET, PHP, and some other web technologies that I will use in order to create a website that can edit videos in HTML5, without Flash. That would be fantastic, because you will be able to use your website on iPads, on Android phones and tablets, and even on your iPhone. Nowadays browsers allow video playing and other nice stuff that will let users place shapes and text on videos, and they will be able to drag them around. As long as the merging part is concerned, the website will upload the videos to the server, where the videos will be merged, and a new file will be created, and finally the user will download it.
It is not easy at all, but it's the most effective and compelling way, as you will be able to reach a lot of users that otherwise wouldn't be able to use the website: more and more people use tablets and smartphones, and they represent the less tech-savvy people, the ones you are trying to reach with your easy-to-use website.