The best way to solve a printer issue is to isolate the possible reasons for a printer to fail.
First step is to reattach the old printer with old cable and old adapter, if it works then the problem is between the wall jack and the printer.
Print the "printer setup" from old printer and compare the setup with new printer, they should be identical for it to work.Dip switch settings should be identical, those switches are so small sometimes they look like they are in the off position when they are actually in between....
compare Baud rate, handshake, etc.
and i agree with TobeThor, in the mean time that you are trying to fix new printer you can disable the cutter from old printer ..