Q: tv gives a black screen every 10 sec

Which Mac Mini? > Finding your Mac OS X version and build information

How much RAM does it have? > Finding your Mac OS X version and build information

Have you upgraded RAM, if so which supplier and what are the spec's of the RAM used?

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1. Shutdown and recheck all of your cables to ensure that all firmly plugged in.

2. Reset the SMC and PRAM.

SMC > Intel-based Macs: Resetting the System Management Controller (SMC)

1. Shut down the computer.

2. Unplug the computer's power cord.

3. Wait fifteen seconds.

4. Attach the computer's power cord.

5. Wait five seconds, then press the power button to turn on the computer.

PRAM and NVRAM > Resetting your Mac's PRAM and NVRAM

1. Shut down the computer.

2. Locate the following keys on the keyboard: Command, Option, P, and R. You will need to hold these keys down simultaneously in step 4.

3. Turn on the computer.

4. Press and hold the Command-Option-P-R keys. You must press this key combination before the gray screen appears.

5. Hold the keys down until the computer restarts and you hear the startup sound for the second time.

6. Release the keys.

3. I mention RAM, because some Mac Mini's have graphic's chips that use the main memory and if the RAM is out of spec it can cause graphic's issues.