You can read about the connection timed out error 10060 on this thread
Basically, i would say you could be trying to connect to a server that doesnt exist (or random server, which some networks arent allowing any more). Check out the website for the network (just put the network name in your favorite search engine) you are trying to connect to and write down some of their server names, then in your main mIRC window, try to join them by manually typing them in, like:
Its possible there is a lot of lag and its just taking a while to connect to that server for you, so you could try going to file/options/connect/options, then click on the RETRY button and increase the time in "if not connected in ____ secs" to a lil higher ( i use 60 secs)
Another possibility is that you have a firewall and arent allowing mIRC or the server ports access thru it. (server ports 6660-6669, 7000-7002 and 113 for identd)
Regarding the winxp/firewall error issue that D3mOn mentioned, thats more likely to be an issue with 10053 (software causes connection abort) error, but wouldnt hurt to disable it to test. Also wouldnt hurt to click on 'How to install" to the left here and double check that you have everything filled into mIRC connect options. btw, you dont need to use your real email addy, and it isnt really a good idea to. just make something up for the part before the @ on the email addy line, (the part after the @ will be your provider, you cant change that) nor should you put your real name in the full name line, make something up.