Unrelated to your problem, but you've got a lot of useless space on the right side of your screen. You can drag those panels around to put them all in a single vertical line, and also you can get rid of the Manifest panel by going to View > Screen Elements and unchecking "Manifest Bar".
Anyway, for your problem: So you're saying you can't select any of the tools. I assume this means the toolbar on the left. And clicking on an entity (such as a prop) doesn't show the prop's information, but instead only shows the Visgroup tab in the properties window.
Sounds like a strange issue. The second half of your issue might be caused by having "Solids" as your current selection mode. On the top right, where it says "Select:" with 3 buttons underneath it, make sure "Groups" or "Objects" is selected. I don't know how to fix the first half of your issue. Perhaps try rebooting Hammer and/or your machine?