I know it's an engine bay fastener, but specifically what is it used to fasten? One of the fasteners in the photo was attached to the battery-starter cable. The other one was laying on the right frame rail.

I'm thinkin' they are vacuum hose fasteners, but that's just a guess.

Also, since these are broken, where can I buy some replacements?

Thanks in advance.

I have those holding up some vacuum lines as well as tidying up some electrical lines. Just where they were intended to go originally...no idea. I just have them bunching together several lines in an attempt to keep the bay just that much more organized.

I have a couple on my car. They are on that top radiator hose and are used to help hold up a couple wires over the fan. I have no fan shroud on the car so the P.O. probably put them there.

I don't know, I think they were originally installed by the factory. I have them on both of my cars like the one you described. It's holding the wires that run to the distributor.