Tub drain problems

I have a tub with a drain that has no 'closing' mechanism. I guess what I'd used to call it was a 'trap', the sort of rod assembly that pushes the plunger up an down and catches all the hair gunk.
So, yesterday, I spent 15 minutes wth a coat hanger and got a ton of hair out of it, because it was draining a bit slow.
After that, it didnt drain. At all. I've poured a bottle and a half of liquid plumber, and draino crystals (yeah, I know not good for the pipes)....
It barely sees to drain at all! So my quesiton is, could there have been a valve or toggle mechanism I hit while clearing it out to effectively shut it? Even if there's no knob on the tub or plunger installed?
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file

HomeOwnersHub.com is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.