Trev,
Your router configs have defaulted back to factory settings. Your ports are shut down again, so you will have to issue a no shutdown on them to get them back up again. That is most likely why you could not ping once you powered your lab back on the next day:
interface FastEthernet0
shutdown
no cdp enable
!
interface FastEthernet1
shutdown
no cdp enable
!
interface FastEthernet2
shutdown
no cdp enable
!
interface FastEthernet3
shutdown
no cdp enable
When the config-register is set to 0x2142, it bypasses the startup-config. It is mainly used for password recovery. You need to have your config register read 0x2102 in order for the router to boot into the saved configuration.
As for the cross-over cable and connecting like to like devices goes; Try to think of it as "like-to-like ports" rather than "like-to-like devices." Remember, some routers (such as the 877 you have) have a combination of layer 2 and layer 3 ports. Switches have all layer 2 ports. So, if you are trying to connect your switch to your 877 router on any of the fa0, fa1 fa2 or fa3 ports, that would be layer 2 port to layer 2 port, which still qualifies as "like-to-like," and warrants a cross-over cable. Here's a good way to remember it: "Can I assign an IP address to this port? If yes, layer 3 routed port. If no, layer 2 switchport." Newer Cisco devices also support something called "auto-MDIX." If the ports on your device have auto-MDIX enabled (which I believe the 877 does by default), it doesn't matter if you use a cross or straight cable as Auto-MDIX senses and adapts to whichever one you use, regardless of like-to-like to like-to-unlike rules. Without knowing the model of your switch I can't say if that will work end-to-end.
As for trying to assign an IP address on fa1/0/1 on your switch; Remember, a switch is a layer 2 device, and layer 2 ports cannot have IP addresses assigned to them because IP is a layer 3 function. This is the same principal of why you couldn't assign an IP address to the fa0 fa1 fa2 or fa3 ports on your Cisco 877 router. For a switch, if you want to assign IP addresses you have to do it on the vlan interface, and ensure you have at least one active switchport on the switch tagged with the vlan the IP address exists on. Below is an example:
int vlan 1
no shut
ip address 172.16.0.1 255.255.0.0
int fa1/0/1
no shut
switchport mode access
switchport access vlan 1
Run those commands and then plug port 1 into another device to bridge it up and the switch will reply when you ping 172.16.0.1. From there you can follow my write up from an earlier post in this thread to get SSH working.
