question on steam radiator leak

I have a very old steam single pipe heating system w/ radiators, seems I have a radiator in the 2nd floor bathroom that is leaking through the ceiling down to the first floor bathroom, it is not leaking at the valve or any of the piping I can see from the 2nd floor bathroom.

The water is dripping down and staining the 1st floor bathroom ceiling. It is a drop ceiling fortunately, but when I took the soggy panal off it looks pretty scary up there, old wood strips w/ what looks to be old old concrete.

Short of replacing the rotted pipe is there any other options here? I have since closed the valve on the 2nd floor bathroom and the leak has stopped, this is only a temp. fix

p.s. this is a 4 family house heated by one boiler. I think it leaks when the steam condenses to water and flows back to the boiler. I guess it wouldn't leak when the steam comes up b/c it is a vapor/gas?? But once it turns to water the leak starts.....

any help or suggestions would be great.

regards,
Harvey

You've got the concept down on how it works...probably will need to replace the pipe; if, that is, you can find out it really is a pipe. Try to find what is actually leaking. I'm not a pro, but you may find that once you start taking things apart, you need to go further than you want to and replace more.