Mac mini mid 2007, hdmi problems

Hi all,

I recently bought a full hd TV by philips and I connected my mac mini mid 2007 to it via DVI to VGA and it works fine (the video quality is not very good, but acceptable). Since I wanted to see some movies in full hd, I decided to buy a DVI to HDMI cable from Amazon. When I connect the cable, the TV is working fine with high quality for like 2-3 minutes, then it turns completely black.

If from the remote controller of my TV I re-select the HDMI, it restarts to work properly for other 2-3 minutes, then again turns black and so on.

I am using also a playstation3 connected to the HDMI and it works fine. I tried switching the HDMI ports, everything works fine for the ps3 but with the mac mini the problem of the black screen keep showing.

I read online that Apple released a firmware upgrade to solve a similar problem with hdmi for the mac mini 2012, but this update does not install on my mac mini mid 2007.

Does anyone have an idea of what I can do?