The machine suddenly will not boot (no chime, no video out)

Hey,

I have a Mac Mini 2011 running OS X 10.10.3. I was watching a YouTube video when the machine suddenly froze and "rebooted". However, there was no startup sound (chime), nothing at all from the HDMI output and the fan starting spinning on high.

I've tried resetting the SMC but nothing has changed. Just a solid power light, no chimes/beeps and the fan spinning on high.

Any ideas?