Verizon uses a different technology for their network, so a GSM (AT&T) device cannot connect to a Verizon CDMA network. The two require different antennas, and the iPad 1 only has the GSM antenna inbuilt.
If you really wanted to use Verizon, you would either have to buy a 3G Verizon iPad 2, or use a Verizon Mifi.