Things connected to the PSU should be CPU 8-pin, mobo 24-pin, all graphics cards with 6/8-pin depending on card, and all peripherals like DVD drive, hard drive, and case fans.
A computer beeping during startup is perfectly normal, usually just POSTing and its a good sign in troubleshooting. You're at least getting that far. The motherboard is what makes the beeps.
If you aren't getting anything on the screen, obviously check the screen first, make sure all connections are solid between case and screen. If that's all good check out the power connections to the graphics card and make sure the fan spins up. Gotta find out what part's not working before we can get a solution.