10053 is rather common, especially with xp users, read thru this thread for things they have tried with success (no one answer fits all, sorry)
10054 basically a glitch somewhere along the connection.
unable to connect, or timed out, could mean the server is down, could be a slowness factor and increasing the line "if not connected in ___secs" under file/options/connect/options under the retry button a bit may help. (i use 60 secs). You mite try connecting on other ports (most have range of 6660-6669,7000-7001). Make sure you have identd enabled and arent blocking port 113, that mite slow things down. Only other thing i could suggest is perhaps try connecting to the ip rather than domain just in case you are having some dns probs.
Since its a cooperate firewall, there is always the possibility they dont want ppl IRCing and may have done some tweaking.
