What type of package (DIL, SOIC, TQFP etc)? Do you not have the PCB?
lol - cross post.
OK, check with a multimeter for connection between the RS232 shell (or the ground pin of the RS232) and the two outer USB pins. That will give you the ground pin. Usually, the opposite end USB pin will be +V, but see what if connects to on the board before just powering it in case it is unusual.
I'm not familiar with such a chip in a 16-pin package. However, you can get most of the pin functions just by checking the connections on the PCB.
If the RS232 side uses CTS, RTS etc then these will go to the chip. For USB D+ and D- (probably the middle two holes) you can just try to connect them either way around; there should be no harm done if they are the wrong way. If it doesn't work, swap them over.
Do you know what driver the PC uses? That might give us a clue as to the chip part number.
Wire up a USB lead (I cut one end off a spare USB lead when I need to wire one) and plug into a Windows PC. If you have the connections correct, you should get the USB detection messages. You might need to find the correct driver though, if Windows does not install it automatically.