The dongle may be a copy protection device without which the software does not work properly. In that case, on the new PC you would have to either have two serial ports, one for the dongle and one for the PLC, or you would have to reverse engineer the dongle and implement it as a software dongle in DOSBox. Or just 'crack' the software protection such that the dongle is no longer needed.

As to getting a serial port working with dosbox on windows, I suggest you do some searches here on the forum. Especially with 64bit windows versions this can be a bit complicated.

1. what is your good old working environment: 386? MS-DOS 5? Win3.11, Win95? - on what OS did you start the software - you didn't tell any details

2. what is your new envronment: x64, Win10, UEFI/Legcy BIOS?

3. the name of the PLC/old Software?
maybe someone knows a solution for exact this old product

4. you need to check your cable - we can't do that for you

5. i don't know how good the serial emulation/put-through of dosbox is (never tested it)?
5.1 does it work if your "newer" system runs on the original Software platform , like plain DOS, Win.311, whatever youre using - you could boot up a MS-DOS/or Freedos Boot-Disk/CD-ROM with the program and test
5.2 does it work if you run the old software in a Virtual Machine like VMWare Player? you can use the same Disk/CD-ROM from step 5.1 for this test

FYI the dongle is connected to the parallel port LPT1. Not a serial port like _Rob said.

If you open up the pc and check the card you should be able to figure out if it is standard db25.

To test the communication I would attempt a more direct approach to listen the port via pyserial or something before adding an other layer of confusion.

I like the idea with trying freedos rather than emulation.