Thanks for the reply and info. Mostly from reading these forums, I do understand that the HP DVD640i could be a LiteOn, Benq or possibly an LG depending on the suffix. As I mentioned, mine is a 640c and it does say "Benq" in small print on the label that is on top of the drive. This thread also indicates that the 640c is a Benq drive:
HP DVD640i (Benq) thread
I was curious as to why the HP website seems to have removed all downloads available for the 640c. Even in the above HP DVD640i thread there are direct links to the HP firmware download, but now when you follow the link the page that opens has nothing for downloading.
Secondly, I was curious if I would get any benefit from flashing my 640c (as a couple have posted they did) with the Benq FW. Like updated media compatibility or bitsetting and booktype. Since you indicated that the last FW from Benq for the 1625 was released last August, I guess there is no need to flash using the Benq FW since it is as old as the JS04 I got from HP back when I purchased the drive.