You seem to have two questions: what tense to use for the verb "to try" in the first clause, and what tense to use for the verb "to receive" in the second.
As for "try," you can use either of your suggested constructions, but they mean different things:
I have been trying to contact you for four weeks
is in the present tense, perfect progressive aspect. It means that you started to try to contact the person, and the effort to contact the person is still ongoing.
I tried to contact you for four weeks
is in the past tense, simple aspect. It suggests that the effort to find the person lasted for four weeks, but that those four weeks happened at some unspecified time in the past. You could be saying this now, and the four weeks you spent trying to contact the person may have happened in 1973.
The second question you have is what tense the verb "to be" should have in the followup. The simplest answer, as you suggest, is to match the tense and aspect of the initial verb. For the present perfect progressive, this would be:
I have been trying to contact you for four weeks, but have received no answer.
...but have not received an answer.
The verb "to get" is probably not your best choice here. "Receive" is clear and easily conjugated; "get" is not only slightly more confusing to conjugate, but in this context may be seen as informal. If you want to use "got," the appropriate forms are:
...but have gotten no answer.
...but have not gotten an answer.
In this case, since the answer has now been received, you could also use the simple past tense here:
I have been trying to contact you for four weeks, but up to now received no answer.
This indicates that the action--the lack of an answer--is no longer a continuing action, but a completed action.
You then add an additional clause, "and was disappointed." This in itself is not particularly idiomatic, although it will be understood. It would be better to avoid the passive voice here, and as others have pointed out, it would be more idiomatic to rephrase this sentence completely, to something like:
...but was disappointed not to receive an answer.
...but, disappointingly, have not received an answer.