Can I set up a new iPhone without the old one charged (I bought the new phone a few days ago and, after trying five chargers, it won't come on and charge

I bought a new iPhone this week and am attempting to transfer info from old phone to new one. One of the reasons I bought a new phone is that it's been very difficult to recharge the phone. The charger end had to be in a precise location. Now the old phone won't charge at all. I've tried five chargers and none of them triggers a charge. Can I set up my new phone without having any charge in my old one?