|I would like to use simple networking facilities (transfer, copying and deleting files) with two computers that only have MSDOS installed in their hard drives|
For a DOS based machine, you would have to install the msclient networking software. Once installed, both machines would have to be connected via a crossover cable and then the TCP/IP settings would have to be configured.
Also, I would like to know if it possible for one computer to sense when the other computer has powered on (to stop its batch file processing and retreive the files from the other PC).
You could use a batchfile to try to ping the other PC. If it responds correctly, then the other PC is up and running correctly. If it doesn't, it's not.