Japanese says no?

If a Japanese says "Hmm I cannot because..but I would like to.." what do they mean by that? Do they really want it or are they just being polite?

Could be anything. Too vague to answer a situational question when only you were there.

The meaning depends on the content of Q, the difference are one of these three usual.

A) Just busy, will not help you well or asking a bit/too late, promised already in that day(s)/time.
B) It is hard request, I'm not responsible, so cannot decide arbitrarily, or mostly illegal(gray what is close black).
C) No money, Or it seems interesting, but I'd like to save money or time in that day(s)/time.

2nd "'d like to" meaning only emphasizes "disappointment",
but using this emotional expression is not only in Japanese,
just Japanese people use it particularly well usual than most foreign countries.

If English is spoken by Japanese, then you already know what he/she want to say.however, no -word used in several ways ,such as:
Dare mo sono jijitsu oshira nai.
Kare wa keshite baka dewa nai
Keshite tabako o suttewa ikenai
Kimi wa jisho o motteiru ka?iie,motte imasen
Kare wa ongaku ka dewa nai no desu ka?iie,so dewa arimasen.
Zenzen chigai masu.....etc