The first sentence is just the copula (am/is/are/was/were) - which is almost always used in English when no other verb is used - with an adjective. There is no action verb to consider here.
I (personal pronoun subject) was (copula 'being' verb) done (predicative adjective)
If we assume the less explicit possibilities (another meaning would be passive voice but is unlikely to be intended), the statement means...
1) My task, activity, or usage of something was complete.
"I was done using the scissors, so I gave them back."
2) My livelihood or involvement in something was over.
"My parents got my report card; I was done (for)."
______________
The second I think could actually be considered either the same copula case or as passive voice:
He (personal pronoun subject) was (copula 'being' verb) worried (predicative adjective)
"He was worried about it." (notice not "by it")
This is similar to "She was married at the time". This doesn't mean she was actually being married at the time; it means she had the attribute of "married".
He (personal pronoun subject) was worried (verb in passive voice)
"The omen worried him." (Active)
"He was worried by the omen." (Passive)
Merriam-Webster lists 'worried' only as a verb, while The Free Dictionary lists it as both a verb and an adjective. Aaa, I dunno, I'm no expert on this stuff - might have figured the whole deal incorrectly.