What is this PS2's model?
Does the PS2 power on (The standby light turns green when pushed)? Does it even show power when you supply power (Red standby light)?
I can only say that you could try to unsolder the modchip, or just try to check for any incorrect wiring/bad soldering (Which may be better, depending on how you see it).
I heard that slimlines (Especially the 75K series) have very sensitive fuses that fuse easily, and will have to be replaced if they have fused from heat from the soldering equipment.
Since you said that it's a crystal chip, I suggest that you get a copy of the wiring diagrams for your modchip for that console's version (E.g. If it's a SCPH-77001 get the diagram for the 77001, or if it's a 39006 the 39006 diagram).
Note that wiring diagrams are usually not the same across different PS2 locale versions, and definitely not the same across different revisions!
SCPH-10000 S. MINOKAMO v1.01 (Defunct)
SCPH-10000 S. KISARAZU v1.00 (faulty)
SCPH-15000 S. KOHDA (With warranty seal!) :D
DESR-5100 S. EMCS