Ideally you would need a layer 3 device to route between the different networks.
Maybe a layer 3 switch, or a layer 2 switch with a router (for a router-on-a-stick type of configuration)..
[L3 switch]-- [Internet VLAN] - [PIX] - [Int.]
| |---[HQ VLAN] - [HQ Router]
|-----[Server VLAN]
OR..
[Router]
|
[L2 switch]-- [Internet VLAN] - [PIX] - [Int.]
| |---[HQ VLAN] - [HQ Router]
|-----[Server VLAN]
Then you configure your L3 device to route between all these VLANs, with proper access-lists, and you'd be set.
If you can't buy additional hardware, you could always renumber the internal interface of your HQ router to be in the same subnet as your other network, and add a static route to your HQ network on servers/pcs that need access to it. It's not a pretty solution, but it would work.