Can I recover when seeing the Spinning Beach Ball

[keriah]

I have a Mini (2009) running Snow Leopard, with SD backups made weekly to a USB-connected external drive. Last week my Mini froze and when I restarted it showed the Spinning Beach Ball of Death. I cannot boot, even in Safe Mode -- I get to the "Log In" step and then the BBall just spins and spins. Is there a way to recover under that scenario? I'd like to try it, even if it's just for the experience.

Question-2: I've now purchased a new (legacy) Mini (2009) with Snow Leopard installed. Can I use the SD sparsebundle file to recover to this different piece of hardware? I looked through the documentation PDF but the restore there talks about restoring to the device that was originally backed up. I'm not sure if things work differently when the recovery is to a different hardware ID.