Can relative clauses be combined with adverbial clauses other than if-clauses?

It seems something is wrong with this PC, which barely a month has passed since I bought.

This sentence doesn't work, because it is not obvious what which is referring to (although logically it must refer to the PC). Rather, rewrite it without the phrase about time passing.

1. It seems something is wrong with this PC, which I bought barely a month ago.
2. It seems something is wrong with this PC, which I have hardly used since I bought it a month ago.
3. It seems something is wrong with this PC, which I would like to return, since I only bought it a month ago.

EDIT

Note that there is a difference between since in your sentence, and since in the respect you would like to use it. If you can replace since with as or because, then it fits the pattern you are asking about. If you cannot, then it relates to a time period, which is something different altogether.

I believe the following sentences demonstrate that one can indeed combine relative clauses with adverbial clauses, using other than if-clauses:

1. Jeff skated slowly, that he should waste time on his journey.
2. Actions speak loudly, when they speak the truth.
3. Sally slept soundly, where she had run feverishly all day.
4. People come here, who love coffee.
5. Strategies work effectively, which take best advantage of the facts.
6. Even high level executives can get pushed out, whose motives are found corrupt.
7. He can advance quickly, whom nature has given good intellect.

Swann missed a big generalization in limiting it to relative clauses and if clauses. Probly it was the "combined with" metaphor that did it. This is not cooking; you don't get a blend, you get a program.

They could have discovered (or rediscovered, depending on the publication date) the Ross Constraints, probably the most important syntactic discovery in the short history of generative grammar.

Details are available in Ross, J. R Constraints on Variables in Syntax, 1967 .

The basic point that's applicable here is that the rule (aka transformation) that forms (relates) relative clauses from (to) their full form, called Relative Formation, is a rule that, as Ross put it, "operates over a variable", meaning that the movement of the relative pronoun to the front of the relative clause can come from indefinitely far down the chained trees of clauses, as long as it doesn't cross certain types of syntactic construction barriers.

E.g, the relative that (which could also be who or whom) is moved from position as object of see

• the boy that the doctor told his receptionist he never wanted to see ____ again

Question Formation is another rule like that

• Who did the doctor tell his receptionist he never wanted to see ____ again?

Except that there are exceptions.
These rules can't cross islands, which are kinds of constructions like coordinate structures

• Frank cooked dinner and Bill washed up ~ *the dinner that Frank cooked and Bill washed up

and complex noun phrases

• She married the man who wrote that book ~ *the book that she married the man who wrote

These exceptions are the Ross Constraints. They apply to pretty much every English sentence beyond The ball is on the table, which contains no islands.