How to replace MS DOS serial (RS232) printer with a computer

We have a legacy data acquisition system running on MS DOS, which prints recorded data to a Serial RS232 printer. I replaced the serial printer with industrial computer using NULL modem cable. Upon sending print command from MS DOS application, application prompts "Printer Error". Is there any handshaking mechanism which first detects the printer on serial port and only then sends data to serial port? How can I implement this task.
Or is there any way out to write the print data to a text file, which I can retrieve when needed.
WOW !! MS DOS Still alive !! Well, it might look for a device of type printer.
You may use any serial terminal software such as TeraTermPro /Putty (3rd party software - which can be downloaded from internet) or equivalent.
Note try to change the Baud rate to match with your actual device type.
If you could read the text in the terminal, you can log them to a file is easy task.
If the print is ASCII then good, else if its a binary, then humans can't read them it will look like garbage.
Good luck and let me know the result.
Your DOS-based data acquisition system very likely uses hardware handshaking and the new computer you're using (and the software running on it) to replace the serial printer is not doing the handshaking.

Here's a helpful post describing RS-232 handshaking:

As Swami suggested, you should try using a serial terminal software, but you need to use one that supports hardware handshaking, as most do not. Here are two that support hardware handshaking:

Br@y Terminal

Termite (with the "Status LEDs" plug-in filter)