If I play Elder Dragon from Dazzling Aurora, can I play it at Dragon Roost Battlefield and pay the 2 power cost?

Yes, you can. Dazzling Aurora only ignores Elder Dragon's base cost (12 Energy + 4 Power). Dragon Roost's [A][A] is an optional additional cost — under Rule 356.1.b.3, additional costs are applied after the base cost is ignored, and Rule 356.2.b treats "may pay [A][A]" as a standard optional additional cost. You declare you're paying it in step 2, pay it in step 4, and Elder Dragon enters at Dragon Roost.