How do you determine if a pre-modifying past participle is a verb or an adjective? [duplicate]

I was trying to edit the question, but I realized that the edit could amount to an answer on its own. So I'm going to post my own answer to my question so I can get some feedback.

While thinking about this question, I've come to realize that broken and murdered are inherently different in that they are allowed to be complements of different form of the verb 'be' when they are used as complements of the verb 'be':

The OP's examples can be rephrased as follows:

a1. I saw a vase that was broken. (= a.)

b1. I saw a man that had been murdered. (= b.)

In order for a1. and b1. to equate in meaning to a. and b., respectively, different forms of the verb 'be' should be used in a1. and b1.

In b2., for example, using the form was, instead of the form had been, renders the sentence even ungrammatical, much less having the same meaning as b.:

b2. ??I saw a man that was murdered.

I don't know how to explain the ill-formedness of b2., compared with the well-formedness of a1., without the analysis that murdered in a. is not an adjective but a verb while broken in b. is not a verb but an adjective.

You can distinguish sometimes, but not always.

• Very can’t come directly before a verb.

• Carefully usually(?) won’t work before an adjective.

Neither of these tests seems to work very well for determining the part of speech of the words broken and murdered in your sentences. None of I saw a very broken vase, I saw a carefully broken vase, I saw a very murdered man, I saw a carefully murdered man sound natural to me.