When will a switch not replace a hub?

We have 12 assorted cables (CAT3, CAT4, and CAT5) going to an
unmanaged 16 port hub. Documentation about the network is nil. Only
5 of the hub lights are lit. I recently tried replacing the hub with an
unmanaged 16 port switch capable of supporting CAT 3, 4, & 5. We put
the cables into the corresponding ports and rebooted all the systems.
Our network connections failed. At first all but one of the lights lit on
the switch. Then 3 more lights turned off. Why would a switch not
replace a hub. I imagine it has to do with more than one network,
addressing, or broadcasting (Captain Obvious).