Why the sentence "Konferans ne zaman başlıyor" is wrong?
Because the translation of your sentence would require to use "when", however, here a specific time has been asked.
To me this is really a paradox, since ne=what and zaman=time, but the meaning of "ne zaman" is when, not "what time".
Can you not say "başlar" for the verb? Like "içer"?
Yes, you can.