The 3 lites are labelled:
D1601 - Red LED On, shows critical temperature fault
D1602 - Red LED On, shows External power connector A was removed
D1603 - Red LED On, shows External power connector B was removed
D601 - Red LED On, shows critical Core power fault
This suggests a power source as the culprit. This, as well as what I've found on other boards, is why I changed out the PSU, thinking that this was a likely culprit. The "old" one was a Rosewill 1000, the "new" one a Rosewill 750.