I've been playing steam games for a good few years now and had this problem right from the beginning. Its sort of annoying but not game breaking.
Basically when I join most servers on valve games (DoDS, TF2, CSS) i get a red warning on the top right after around 20 seconds saying
"warning connection problem
auto disconnect in 25 seconds" (counts down)
Once I disconnect I get a box saying "Lost connection to server". Then exactly 2 minutes after I join a DoDS server (3 minutes with TF2), my name disappears from the server player list and I can join again now with no problems. With the private server, I instead get the message "steam validation rejected" and have to reconnect after 3 minutes.
Im relatively certain this is a problem form my end (unless of course my computer is perfect and every other inthe world is messed up) and possibly a router issue. Unfortunately the steam support page got a redesign and now I cant seem to find shit there.
If any of you have a solution then great but please talk real nice and slow because I'll probably be lost after the a few words as I usually have no idea what your talking about once the technical jargon starts.