There is no reason you shouldn't be able to look at the filenames on the disc; I'm not sure how you are attempting to do that but if you open windows explorer you should be able to see the filenames. If it automatically tries to run when you insert the software then you may need to close that but you should be able to see the filenames in windows explorer.
Unfortunately, I do not believe you will get that program to work, even in compatibility mode; most likely because it tries to reference resources in a way no longer supported. You may be able to buy updated software from the manufacturer or you might be able to get it to run in a virtual XP environment but I don't know that for sure (if you have W7 Professional, Ultimate, or Enterprise then Microsoft's version of Virtual PC - XP mode is available for free download).
Is the headset from Microsoft as well? Please specify the make and model of headset and (I assume) a USB? receiver that wirelessly connects to the earpiece. Also what is the exact name and version of the software? There may be new drivers to allow the ear-piece and receiver to function in W7 and Microsoft has likely upgraded or replaced the Live Chat (I found something in my searches called Life Chat so please clarify it is Live Chat along with version).