Let's back up a second.
A) What HP model is it? (P/N. Product Number. Back of desktop computer tower)
B) What model number of Intel quad core is it?
C) What are the manufacturer ID number/letters on the ram memory module/s?
I need to know what Northbridge chip is used on the motherboard, to know if it will support the particular Intel quad core you're trying to use.
This I can hopefully obtain from HP Support, by looking at the specifications for the motherboard.
(This technology does not apply to motherboards that support the Intel Core i3, Core i5, Core i7, and Core i9 processors)
The Northbridge chip is part of the motherboard chipset.
So aptly named, because on a desktop computer motherboard it sits to the 'North', for one.
(Under the Processor)
[ Chip and Chipset are slang terms for I.C.
The Northbridge chip handles the faster capabilities of the computer.
It handles the Processor, Ram Memory, and High-speed graphics.
AGP and PCI-Express are high-speed graphics technology.
A graphics card plugged into a PCI slot, and Integrated Graphics, is Not high-speed graphics.
The Southbridge chip handles the slower capabilities of the computer.
List of Intel Chipsets, and more specifically the one's that can handle Intel quad core processors,http://en.wikipedia.org/wiki/List_of_Intel_chipsets#Core_2_chipsets
Make sure the Ram Memory you installed is Compatible.
If the motherboard supports 4GB of ram, make sure it is in the correct ram slots if using two sticks of ram, or four sticks.
There HAS to be a ram memory module ('Stick') in Slot 1. (DIMM 1)
EACH ram memory slot has a Maximum Amount.
For example if there are 4 ram slots, and the Maximum Total Amount of ram memory is 4GB, each ram slot may have a maximum of 1GB.
It may, or may not be that you can use Slot 1 and Slot 2, and use two 2GB sticks.
Always go slow when upgrading.
Install the Processor first, boot the computer up, see how it works.
THEN shut the computer down, unplug from power, observe Anti-Static Precautions, and install 2GB of ram memory.
Install the other 2GB.
BIOS has to recognize the changes.
Are you sure your Power Supply is adequate to support the quad core, and the added ram memory?
Post back in a Comment.