I'm really not sure. My advice is that if the wires from the replacement blower motor don't match the wires from the original blower motor, that possibly you were provided the incorrect blower motor. Just because the motor itself might fit/bolt in doesn't mean it's the correct one. It could be for a different year Corolla than your own, which would explain why it bolts in, but the wires don't match.
Again, I'd check with your auto parts store and have them double check the listing/part number for the blower motor recommended for your Corolla. The blower motor they provided you doesn't happen to be a made in China part, is it? If so, that's not a good sign at all as made in China parts are notoriously low quality. If it is and it were me, I'd return the part and get my money back on that point alone. Made in China parts, in my opinion, (have to keep it legal),
are junk.
If all else fails, you could try a used blower motor from a junkyard from the same year Corolla as yours, then you're guaranteed it's the right blower motor and it will be much less money than a new one. Below is a link where you can find junkyards in your area and the part you need -
http://www.Car-Part.com
So if you can't get the current blower motor working, I recommend returning it and getting your money back, as there's something wrong with it. I wouldn't mention you had problems wiring the motor in, or they may claim you fried the motor due to improper installation and there goes your refund.