Which CPU and what memory are you running?
First gen Core is weird about memory, see for example https://www.os2museum.com/wp/nehalem-and-4-gbit-ddr3/
Rule of thumb is that on 32nm dual core cpus (both desktop and mobile) the largest DIMMs you can use are 4GB with 2Rx8 organisation (same as 4 series LGA775 chipset, as the memory controller is roughly the same), whereas 45nm quads may or may not run 8GB 2Rx8 DIMMs, it depends on the CPU, the motherboard, how lucky you are and what is the atmospheric pressure.
Single ranked 4GB sticks WILL NOT run on a 32nm, will probably be detected as 4GB from the SPD data but will crash horribly shortly afterwards from my experience. Will probably work on a 45nm quad as a dual rank 8GB stick is just two single rank 4GBs glued toghether.
If you ask me I'd say put four cheap 4GB 1333 2Rx8 sticks in and call it a day, you'll have more than enough ram for anything you can do with such a machine as long as you're not running it as a virtualisation host.
Latest bios for the MS-7613 is 6.18 at https://ftp.hp.com/pub/softpaq/sp56001-56500/sp56189.exe