iMac start beeping, black screen

The beeps indicate that your iMac is failing the Power-On Self-Test (POST)

This test checks the Mac’s hardware and RAM (random access memory). It resides in the Mac’s ROM (read-only memory) and runs at startup (though only from a currently shut-down Mac; it won’t run if you simply restart a running Mac). If POST detects a problem, the startup sequence will probably halt almost instantly. In addition, you’ll hear one of the following sounds:

• One beep. Indicates that no RAM is installed or detected.
• Two beeps. Indicates that an incompatible RAM type is installed.
• Three beeps. Indicates that no RAM banks passed memory testing.
• Four beeps. Indicates there’s a bad checksum for the remainder of the Boot ROM. (Checksum refers to a method of determining whether data is corrupt.)
• Five beeps. This means there’s a bad checksum for the ROM boot block.

If you are currently getting 4 or 5 beeps, the issue is going to be the iMac's system board ROM. Most likely a system board failure.

I would try resetting the SMC, and try resetting the PRAM again ... if possible. However, if you don't have a workable keyboard, you may be out of luck.

Ref:

• Reset the System Management Controller (SMC) on your Mac- Apple Support
• How to reset NVRAM on your Mac- Apple Support