It depends on what the motherboard supports and what power supply you have.
I've looked at multiple Families of processors that work for the LGA 775 socket.
The two processor families that are comparable are the Core 2 and Xeon.
The Xeon family is more reliable,
Assuming your PC supports Xeon processors.
Xeon processors are used in workstations so they're the go to if you're going to run your pc for multiple hours
plus they're affordable.
If your motherboard is only dual core.
I'd definitely go with the Intel Xeon E3110,
if you buy it on eBay you won't break the bank getting it and it runs at 3Ghz.
If your motherboard supports a quad core CPU.
I'd go with the Xeon X3380
seeing as it is available at a reasonable price on eBay.
It also has SSE4.1 support, the Q6600 doesn't.
Intel Xeon E3110 specs
Intel Xeon X3380 specs
Intel Core2 Quad Q6600 specs
X3380 vs Q6600
Assuming you haven't updated your Bios, I recommend updating it asap in case they added xeon cpu support to your Motherboard.
---Edit---
Forgot to mention.
Your motherboard must support the Front Side Bus speed of the cpu.
In the case of both Xeon CPU's, unless the chipset supports a 1333mhz fsb it won't work.
based on the reported chipset and on this link
here it should work given i see some 1333 fsb CPU's on the list.
Another thing i'm concerned about is if your motherboard has the voltage regulator ICs to support quad core CPU's.
Given the screenshot doesn't list the motherboard none of us can find that out. please open command prompt as admin and type "wmic baseboard get product,Manufacturer,version,serialnumber" then screenshot the results if you can find the motherboard model number somewhere.