intel i915 chipset

The 915 supports dual core cpus all day, c2d or PentiumD etc. What it won't support is the quad core cpus like the q6600 or q6700 that the slightly upgraded 945 chipset will. The 915 was the cheapest available board at the time, the lowest end available, but supported the most commonly used cpus, so was mass produced for everyone from Sony to HP or Compaq or Acer.

I can't see on speccy your motherboard, or I missed it, but depending on what graphics port you have will determine your best option. Many of those older 775 boards with ddr2 used a AGP graphics, it's pretty short. The newer boards used the updated x16 which is a lot longer.
 
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your motherboard information is incomplete. you will need to open the case of your computer and look for a label on the main motherboard to know who manufactured the unit. Intel chip set are used oin all sorts of systems. Also does your computer have a bdan name on it perhaps like Dell ? or HP ? or was it a custom built system ?

As for the chipset i915p there are a great many deal that use that chipset, I will need the model number from the board or brand name of your computer

 
The pentium e2200 Conroe is a dual core cpu. The Conroe family includes some c2d, PentiumD. Some of the low grade, early 945 don't support the c2d only P4, Celeron and PD, but newer designs upgraded that. Was about that time when boards also switched to pcie x16, so chances are decent if op's board is an older 915 that it's still AGP.
 
The Intel 915 Chipset does not support any dual-core CPUs.

Users have installed unsupported CPUs that boot up but don't operate correctly.

Anyone who says they do support dual-cores needs to present at least one motherboard as an example of their claim.

The 945P Chipset first offered dual-core support in May 2005. It was an updated version of the 915 that added support for Serial ATA II, RAID mode 5, an improved memory controller with support for DDR-II at 667 MHz and additional PCI Express lanes. Support for DDR-I is dropped. Formal dual-core support was added to this chipset.
https://en.wikipedia.org/wiki/List_of_Intel_chipsets