Have you tried clearing the CMOS?
The chirps and and beeps you hear will be coming from a buzzer located besides the CMOS battery (black cylinder with a hole on top). You'll hear repeating chirps if the system is on a boot loop.
Somewhat unrelated to your hardware but I, too, recently upgraded from an i5-4570 to an E3-1285v4 on my home-built server (Gigabyte Z97-D3H). I initially encountered the boot loop (slow repeating chirps) until I decided to remove all power and cleared the CMOS. After that, everything booted up to BIOS/UEFI. I loaded up Optimized defaults, and It