This is not difficult. You are wasting time on the wrong approaches.
If you have PanelView and a 1761-Net-AIC connected, then the serial port of the SLC-5/05 is assuredly configured for DH485 protocol. The only way to connect using a serial 1747-CP3 cable and the 1761-NET-AIC is to configure the 1747-PIC/AIC+ driver in RSLinx Classic.
The settings are nearly trivial; select an unused node number (let's guess the PLC and PanelView are 1 and 2, so make the PC Node 3) and use 19200 baud.
The bad news is that this driver can be finicky in Windows NT/2000/XP. You've already read that it needs to run as a service, and it won't run at all over a USB/RS232 converter.
The right way to connect to an SLC-5/05 controller is using Ethernet.
Your PC's firewall is preventing the BOOTP Enable command from getting through. If you have the permissions, configure the Windows Firewall or other firewall to open TCP ports 67 and 68.