What's the relation between the serial connector RS232-DB9 and 10 pin cable?
Since the manual says not to use flow control all you likely really need is to find TX, RX, and ground and connect a terminal at 38400,N,8,1 and to disable flow control in your PC terminal program.
The additional pins should not need connection at all, provided that you disable flow control such that your PC is willing to transmit with them unconnected.
You appear to already have candidate connections for TX and RX and Ground on pins 2, 3, and 5.
You may need to consider a cross-over between RX and TX depending on how they are defined. (Confirmed in comments - this was the issue)
It's also entirely possible that your issue is not with the serial connection, but with the firmware of the device or the software you are using on your PC or anything like an outboard USB-RS232 adapter.
Do make sure you are using a USB-RS232 (eg which came with a 9 pin connector on it) and not a logic level USB-UART sold for Arduino projects...