plain OM is right, if it's an H6, it does have timing chains, but the engine would have to be dismantled to see them.
Subaru had only two engines in 2003, an H4 and an H6 (named so because the pistons and crankshaft form an H instead of a V or an I, which would make a V6 or an I6). If you have a 6 cylinder, you have the H6.
The only reason you would have zero compression in any or all cylinders is if the valves were stuck open, or if the valves were bent...in which case I'd think you'd still have a tiny bit of compression left. Either case, it's timing related.
If it's not timing related, compression has to be effected by either a blown head gasket or you don't have spark plugs. Even if you had a blown head gasket, the car should still start. The only thing left is the spark plugs. Without spark plugs you have no compression and the car definitely wont start.
By process of elimination I have concluded that someone stole your spark plugs while you ate dinner. And considering how difficult and time consuming that task is on the H6, the thieves must have been quite good.
lol ok, obviously I'm joking, but seriously, either you have no spark plugs or the information your mechanic has fed you is wrong.