The beeps may be BIOS/POST error codes. The number, frequency, and duration of the beeps identify the exact nature of the error. The meanings of the "beep codes" vary by BIOS manufacturer; this Google search
returns a number of sites which list the various code tables.
In terms of determining the source of the problem, have you attached another (known-to-be-working) monitor to the questionable video card, and have you tested the moitor on another system with a working video card?