Your inxi output clearly shows that your graphics card is working. If it weren't, you would not have GLX information. It also shows your driver 'intel' successfully loaded. So X.org is working fine.
You have to define 'not working' slightly more accurately in this case.
You are clearly running inxi in your desktop, which means, your graphics are working.
Further, you do not have two graphics cards in the system, or you would see both of them listed in the inxi output, so that's not the issue, unless of course one of them actually failed on a hardware level, then you wouldn't see it.
Further, xrandr is clearly working, and running fine, and you have the expected screen resolution of:
So that in essence means that in fact, your desktop and graphics card are working, visibly so.
So you'll have to explain more clearly what you expected to happen compared to what is actually happening.
If I may, I'd like to quote from the famous Debian irc factoid, which is unusually witty given how serious debian tends to be:
doesn't work is Look buddy, "doesn't work" is a vague
statement. Does it sit on the couch all day long? Does it
procrastinate doing the dishes? Does it beg on the street for change?
Please be specific! Define 'it' and what it isn't doing. Give us
more details so we can help you without needing to ask basic questions
like "what's the error message".