John,
That sounds like an ASUS hardware problem, not a HP issue. Personally I'd get on eBay and look for a HP DVD writer that has a pretty high part number, starting with a 7 if possible. You can search under HP DVD writer, HP optical drive, HP CD, etc. At least get the ability to read/write DVD. These are so inexpensive these days, and they generally are plug and play.
I've never seen a SATA optical drive not be recognized immediately by the workstation. Sometimes there may be a special driver needed, but in that case at least the drive will generally show up in Device Manager with a "yellow bang" excalmation next to it.
There are some of these HP optical drives that have HP firmware updates for them.... google can usually find those updaters. I've seen a few older ones that would work for installing XP but not W7, W8, W10, but at least they'd show up when plugged in.
