Can a computer with 2 network cards have the same IP address for both

Yes and no.

While e40 is correct in thinking that IP addresses should be unique within a routing domain (i.e. there should ever only be one 10.0.0.1 present on your network - see RFC 5889) you can have multiple hardware devices underlying that single IP address. This is generally done with Link Aggregation Control Protocol (LACP). LACP can function at any of the three lowest OSI layers which of course includes IP. The method in which the IP address is "resolved" (at Layer-3) to which specific MAC address (at Layer-2) for frame delivery is largely implementation dependent (although generally it's round robin).

You could configure IP address aliases on each device so that each NIC could be reachable individually or through the "virtual" IP address that represents the bonded NIC (both devices).

The NICs must each have a separate IP-address, these should normally be in separate subnets.

The exception would be when you are using something such as channel bonding or some hot-failover redundancy system.