Error 0x80070035 simple means "Network Path Not Found" which is what your problem is. It could be a variety of issues such as network connectivity, a name resolution issue, NetBIOS over TCP/IP, or firewall related.
I am still not clear on your basic network health. I've asked if you are able to PING each of the computers. I do not beleive that you have validated that this is the case. Can you ping by IP and by Name?
If its name resolution related, you should be able to access the share by supplying the target computer's IP address in the UNC path.
For example, instead of trying \computer1\sharename, try \ipaddress\sharename.