Since this HT 'All in One' system lack HDMI inputs, you will need to find another type of connection that would send along a digital audio signal from your desktop to the Philips unit. I don't see anything obviously marked as 'digital audio output' in your screenshot from the back of your desktop PC. Bob (who also replied) could probably recommend sound card options if you provided more specifics on the make/exact model # of the PC.
Basically, there's no reason why a PC or other device couldn't pass along audio to this rig, since the specs indicate it's possible via either a digital optical or digital coaxial input. Video output from a PC is a non-starter since there are no video inputs behind the Phillips. ARC may also be a non-starter depending on which HDTV you own, and as Bob has suggested, since ARC is hit or miss.
Hey! I recently got the Philips HTB3550G and would love to connect it to my PC, considering I use that a lot more than my TV. I was wondering if it was possible, and if so, what I need for it to work. Here the ports I have available on both my system and my PC:
http://i.imgur.com/g0iSCqW.jpg - http://i.imgur.com/O0AQuoQ.jpg
This is copied from the system's manual:
Front Connections: Audio in, Hi-Speed USB, Microphone In
Rear Connections: Digital Coaxial in, Digital optical in, Easy-Fit Speaker Jacks, Ethernet, HDMI 1.4 output (ARC), AUX in, Fixed FM Antenna, Wireless Rear Audio
Integrated Connections: Bluetooth, NFC
Appreciate any help, thanks in advance!