I know you said 'endless stream', but if you listen carefully, is there any pause in the sequence (e.g. after the 6th, 7th, 8th etc). This will help pinpoint the exact error code.
"2.Q:What’s the meaning of AMI BIOS Beep Codes?
A: The following are AMI BIOS Beep Codes that can occur.
Beep Code Descriptions
1 short Memory refresh timer error.
2 short Parity error.
3 short Main memory read / write test error.
4 short System timer failure
5 short Process error.
6 short Keyboard controller BAT test error.
7 short General exception error
8 short Display memory error.
9 short ROM BIOS checksum error
10 short CMOS shutdown Read/Write error
11 short Cache Memory bad"
(From the ASRock web site).