In English reported speech the present tense in the actual words spoken becomes the past tense in the words when they’re reported. The reported forms of those two examples are ‘He asked me what kind of computers I had’ and ‘She asked me what music I liked.’ The situation has changed. The speaker reporting the speech is referring to something that was the case in the past, if only in the very recent past.
As others have said, this is not invariably so. As the authors of the ‘Longman Grammar of Spoken and Written English’ write:
The original speech or thoughts may have been in present tense, but past tense is usually used for the report . . . Although this use of past tense in reported speech is common, reported speech also occurs with other tenses. [The present tense emphasizes] that the circumstances expressed . . are still continuing.
But if in doubt, change present tense in direct speech to past tense in indirect speech.