I'll also add to Kevin's answer (besides moving this to the firewall topic)...
Can you share files to the PC that is hosting the accounting software by browsing in Windows Explorer? I'd first want to confirm that File and Printer Sharing is working.
Then, as Kevin pointed out, if the Peachtree software on the host PC needs ports open for it to "listen" on, these ports would need to be allowed in addition to allowing the software.
-steve