In my 5 year old natural gas fed steam boiler, most of the burner tubes and support tray have rusted away. The boiler is dirty and plugged between the sections and its supports are rusting. It replaced an identical boiler that ran for 25 years without a problem.

The most serious problem seems to be that the condensate return lines are almost completely plugged with a greasy, oily substance. What is that? Where did it come from?

No changes to the system (other than replacing the boiler) were made. The chimney is clear, the make-up water is clean.

I'll replace the boiler, and make sure the pipes are cleaned out. But what went wrong, and how do I make sure the problem won't return?

Thanks..

Sounds like a moisture condensation problem on the external damage.

The goop inside who knows. I would get a sample analyzed
To find out what it is and what chemical is needed to clean the system and what chemical is needed to be fed into the new boiler to prevent this problem in the future.

See "Rollout fuse keeps blowing".