What happens if two computers have the same MAC?

It's going to be dependent on the switch in use by the hosts in question. The hosts themselves have no awareness of the infrastructure to which they're connected and don't know which switch port the destination hosts are connected to. How exactly the switch handles the same MAC address registered on different ports is a matter for the particular switch in use. My guess is that the switch will forward the traffic to both hosts.

I disagree that there will be an ARP storm. ARP is used to resolve IP addresses to MAC addresses. Your scenario doesn't suggest that IP to MAC resolution is going to break, only that 2 different IP addresses are going to be resolved to the same MAC address, which isn't in and of itself a problem as a single host may have multiple IP addresses. Your case is that 2 different hosts with different IP addresses may have the same MAC address, so packets may be misforwarded but that won't cause an ARP storm.

You don't seem to know how a switch works: It learns MAC addresses! Once it sees an address coming from a port, it will direct the traffic for this address only to this specific port.

In your case this means the two hosts will see only part of the traffic, depending which host sent the "latest" packet. The result will be very ugly networking problems. Do not expect the switch to handle this situation: MAC addresses are supposed to be worldwide unique.

A hub may work -- they simply spit out the packets on all ports except the one where it came in -- but these are very rare for 100MBit and non-existent for Gigabit. And of course half-duplex.