It seems that you need some assistance in order to hook up your HTPC to your Slingbox PRO.
First, we recommend you to check if this device is included on the supported devices list. The following link will allow you to check the compatibility.
The Slingbox PRO will allow four connection types: Coaxial input, Composite input, S-Video input and HD Connect cable input.
These are the available and supported inputs. If they are already in use, you'll need to get rid of any of the devices connected to your Slingbox PRO. Just keep in mind that the available ports you mentioned (HDMI, DVI and VGA) are not compatible with the Slingbox (any model).
Just to clarify, the available port on the back of the Slingbox PRO is for the HD Connect cable (not related to the HDMI cable).
You could purchase an HD Fury3 (hdmi to component video adapter). Out of the HDPC's hdmi output tpo the HD Fury3 adapter, then out of the HDFury3's component output adapter to the slingbox's hd connect cable adapter's component video input.
*REMEBER the slingbox pro does NOT have an HDMI connection. What appears to be one is actually used to connect the "HD Connect" Cable Adapter"; thus the need for the HD Fury Cable adapter in oder for proper conenction.
Also it would benefit you to updgrade to the Slingbox Pro "HD" as the quality of remote streaming will increase as well as the ability to stream actually HD (given you have the minimum required upload bandwidth to do so).