Q: mac mini 2011 yosemite will not turn on

What exactly happens when you startup the mac Mini?

Can you boot in Target Disk Mode?

How to use and troubleshoot FireWire target disk mode - Apple Support

If yes then you can likely clone that did to your new one but yo may have to just use Migration to move the data and apps

Move your content to a new Mac - Apple Support

You may have to reenter the activation codes for various apps though

You can also during initial setup of the new Mac migrate from TM backup but you may have to reenter activation codes for various apps

1. First off, we do not know which Mac Mini you have. see > How to identify Mac mini models - Apple Support

2. Then try everything at > If your Mac won't turn on - Apple Support before you make up your mind that you need to buy a new one.

3. While Time Machine can restore all of your User Data, it lacks some of the better options that a CarbonCopyCloner or SuperDuper clone can provide in exactly this situation.

The poster's subject says 2011 Mac Mini. He may have the graphics problem

Oops.. thank's, I missed that in the title.

Also good point, if he has the 2.5GHz model with the AMD Graphics.

Yup, seems like you will have to take the disk out and connect to a dock or place in an enclosure or restore from TM backup.

Yes, I old just use Setup Assistant during initial setup of the new Mac and restore from TM backup.

If you migrate after initial setup a new users will be created with the migrated data/files

You asked "That should be bootable...yes?"

Yes, the HD will be bootable on any Mac that can run the OSX version that was on the HD.