You aren't testing my patience. I just wanted to be sure I fully understood the situation. I think that i do.
I take it, then, that you haven't made an effort to reinstall Lion? If you haven't then you might give this a try. If the hard drive on the Mini is OK this may work. If the first attempt at installing Lion did not fail completely, then you should have a Recovery HD on the HDD. So start with this:
Reinstalling OS X Without Erasing the Drive
Boot to the Recovery HD: Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
Repair the Hard Drive and Permissions: Upon startup select Disk Utility from the main menu. Repair the Hard Drive and Permissions as follows.
When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the main menu.
Reinstall OS X: Select Reinstall OS X and click on the Continue button.
Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.
If this does not work because there is no Recovery HD or it's corrupt, then check this document: Computers that can be upgraded to use OS X Internet Recovery. If your Mini is on the list of usable Macs, then you can do a full Internet Recovery:
Install OS X Using Internet Recovery
Be sure you backup your files to an external drive or second internal drive because the following procedure will remove everything from the hard drive.
Boot to the Internet Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND-OPTION- R keys until a globe appears on the screen. Wait patiently - 15-20 minutes - until the Recovery main menu appears.
After the recovery menu appears select Disk Utility. After Disk Utility loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the main menu.
Reinstall OS X: Select Reinstall OS X and click on the Continue button.
Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.
You will note that you are doing the same thing as the first set of instructions, except this time you will get the network Recovery HD.
Now, I would need more information on this Snow Leopard disc image you have. However, I'm out of town for a wedding tomorrow, so I don't know how much time I'll have to see how this goes for you. If it doesn't work, then you will need to tell me all about your Snow Leopard disc image such as what it's an image of. If it's an image of a Snow Leopard installer DVD, then you could clone it to a USB flash drive from which to boot your Mini and install Snow Leopard.
Your other option might be to use Target Disk Mode to clone your MBP's hard drive to the Mini's HDD. This assumes the OS on the MBP is compatible with the Mini. Your MBP must have Firewire ports.