Yes - what you can see as a 'washer' still in the seat tube is the remnants of the suspension seat post. You have to get that out. It is probably not stuck but needs upward force to extract. I'd fashion a straight piece of metal with a hook (U bend) at the end which will fit through the section of tube left in there and fiddle around till I got a catch, and then pull. A straightened heavy gauge metal coat hanger would be my first try.
@cyberknight's 'upside down and shake' may work: try that first.
I suspect the seat post is FUBAR and you'll need another. Go for a 'normal' one (diameter possibilities as per ^^^).
If no success, your local bike shop will pluck this out in two minutes, and sell you the right size seat post as a replacement.