RE: Dell t5500 workstation diagnostics lights 2 3 4 blinking no display
Did you inspect the two CPU riser sockets for debris, bent pins or other anomaly? Does the unit think there should be a riser inserted - meaning would inserting a riser card trigger a mechanical switch to indicate dual CPU and is this switch broken?
What was going on around the time the problem first occurred? (I assume it was working for you before.) Were any components changed or was the unit location changed or moved/transported around the time the issue first happened?
Not sure where I'd go from here. Checking/reseating cable connections and trying to swap motherboard and/or PSU is probably what I'd try next...