Windows

With a peer to peer network, there's not a limit to the number of nodes (computers) that can be configured. (At least, not that I've seen or encountered.) There is, however, a fundamental limit to the number of queries that may be processed by a fully distributed network in terms of bandwidth requirements of the slowest nodes.

This is what you are experiencing.

If a query requires Q bytes and the slowest links have bandwidth B bytes/sec, that node can only process B/Q queries per second.If a node in a tree topology cannot process the query, it effectively truncates that branch from the tree and results in network fragmentation.

This is a fundamental limitation in peer-to-peer networking. If every machine is responsible to handle every query, the network paradigm is doomed to suffer this limitation irrespective of the available bandwidth.

Look at this very nicely illustrated article on peer-to-peer network design considerations. I think it may answer all your questions.

http://aeolusres.homestead.com/files/

(REMOVE SPACES from the pasted URL.)

If the machhine that "all the files in the office" is XPPro, or Win2KPro, or NT4Workstation, then yes, there is a limit of 10 concurrent connections. Only 10 machines can be connected to a Windows desktop OS machine.
NT4Server, Win2KServer and .NETmachines do not have this limitation.

hope this helps

You didn't say the OS on the central file server. If possible, check local connections on it (users), and disconnect all. Sometimes the OS thinks there are more users connected than is actually the case due to startup/shutdown probs. and hangups.
It may help to map network drives to the file server on each system. You might also try installing a second NIC on that machine.
Using TCP/IP only? Get rid of unnecessary network protocols like NetBeui.
Using any switches, or just hubs? Consider upgrading to newer switches. Upgrade NICs to 10/100 if any are still using 10mbps cards, especially if they are ISA cards.
Remove any unnecessary services running on your machines that use network bandwidth.
Do your users have internet access?Tell them to use for business use only!!