First of all - welcome to CMN!
The projector is controlled by an RS232 port. You will need the correct connector type as specified in the manual (look on the rear of the projector to double-check the type).
The manual shows the pin-out for the cable between the projector and the PC (page 33). It looks to be a simple pin 1 to pin 1, pin 2 - pin 2 etc. for all 9 pins and shield/body.
RS232 comes in different 'flavours'. There is the usual transmit and receive lines but there are also hardware handshake lines (RTS = Request To Send, CTS = Clear To Send, etc.). The manual does not make it clear if these hardware handshake lines are used by the projector or not. As the manual identifies a cable with ALL connections made, you should make or buy a cable as specified by the supplier to be on the safe side. If the projector does use hardware handshake lines - and you have not wired them up to the PC - then the projector will not be able to transmit data or may not think that an external device (e.g. the PC) is connected.
The other usual mistake is to connect transmit on the projector to transmit on the PC and receive on the projector connected to receive on the PC. This will not work for obvious reasons! Follow the correct pin-out given in the manual in the first instance.
You will need to connect the projector to the RS232 connector of a PC.
The RS232 port can be configured for different parameters (e.g. speed, parity, stop bits, number of data bits). The manual gives the configuration that the projector is expecting as 19200 bits per second (baud) no parity, 8 data bits and 1 stop bit. The serial port on the PC must be set to the same configuration.
You will also need some software on the PC to control the projector. PCs do nothing without software! I have not used the Omnivex 4 package but I have helped someone on CMN get a similar software package running. I can't find the message thread immediately - but I will have a look later and post a link to it. The protocol for your projector and the one I have helped with previously looks identical.
Some means should be provided within the software package on the PC to configure the serial port parameters. In addition, there are a number of different protocols in existence for driving projectors. You will have to configure the software package to either drive your specific make and model of projector - or identify another projector configuration that uses the same communication protocol as yours.
If your PC has multiple serial ports then they will be labelled as COM1, COM2 etc. It is important to connect the projector and configure the software to use the same serial port!
The PC software package may also have some configuration parameter for hardware handshake lines. If so, try the set-up with the lines ON and then (if that does not work) try OFF.
In terms of the length of cable - you can get away with anything providing it works! Personally I would stick to what the relevant Standard says in terms of cable type, connectors and cable length. If you use inferior cables or break the recommended distances then the safety margins will be degraded. This maybe OK at the time of the install - but if someone then adds some other electrical equipment to the room you may find that the system starts to become unreliable as the safety margins are now negative.
Hope this helps?