If you're having troubles opening or editing a photo, the easiest thing to do first is to try PicMonkey in Google's fantastic browser, Chrome. Install it free here: http://chrome.google.com
Next try opening one of the sample photos on the Home page. If the photo opens, click the Upload button in the top toolbar.
If you want to stick with your current browser (should be Internet Explorer 9 or the latest FireFox), please make sure you have the latest version of Flash: Get Flash Player from Adobe.