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After it's done burning the disc it goes into a VERIFY mode. UH OH.

What blank discs are you using? I am not blaming them for your issues, if your Mac can't handle them it should be able to be sensible about it instead of locking up.

But I am just curious what they were. Did you try different brands?

On a side note, you could pop in the Apple OS X DVD that came with your Mini and see whether it will run the Hardware Test (see the instructions printed on the disc for the magic key combo to run it). This may tell you how dead your Mac is.
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Hussein