When the code opens the port, mode says the device is not available. So at least perl grabbed the right device, but I can't tell what the settings are.

Did you try setting the port then closing it before using the mode command? They (usually) retain the last set of settings until something changes them.

Another old technique for setting up serial ports initially is to do everything from the command line:

mode com3: ...
copy con com3:
type whatever the device is expecting here
^Z

## see what response you get
copy com3: con
[download]

If you need to send or receive binary , then judicious use of /b on the copy commands may be in order--though it is a pain entering Alt-nnn, Alt-nnn.

Also, if the device doesn't respond then you will probably have to kill cmd.exe from the task manager to get control back.