I know of only one way that this can happen in windows, and has nothing to do with Steam other than their not-so-great decision to install all content into Program Files.
If you are on Windows 7 or Windows Vista, and you have UAC set to ON, then change it later to OFF, this can happen.
UAC does thing evil thing where if a program tries to write to a "protected" area like Program Files, EVEN IF YOU ARE ADMINISTRATOR, when you get a UAC prompt and give permission, it actually writes any files that would normally go into that directory into a "virtualized" directory somewhere else.
If you turn off UAC, that will no longer happen, and as an awesome bonus, it will no longer know about the files that it virtualized.
So in your case, if you had UAC on, installed a ton of games, then later got sick of UAC and turned it off, this would happen as you described.
See the second paragraph in "Features" in the article on User Account Control.
If you have done this and turn on UAC again, your content will come back, but be a TOTAL mess because if you've downloaded more stuff with UAC off, then that will be invisible when you turn UAC on, and vice versa.
this drove me a little crazy once before I realized what was happening.
i'm curious to know if this is your issue.
Presumably your copy has some method of circumventing Steamworks that persists even when you attempt to download changed files from Steam. Backup your saves (located in "C:\Users\Your Username\Documents\My Games\Borderlands\SaveData" for Windows 7/Vista and somewhere similar for XP) and remove Borderlands entirely. Ignore step one and step three, simply let Steam install the game. This should restore full Steam compatibility.
Best Answer
A friend had a same problem. I asked him if it's still happening and he said that he found out windows was allowed to turn off the network adapter. This probably only applies to wireless adapters, especially USB ones.
How to fix that:
devmgmt.msc
This is not steam specific. I will test that no other problems happen.
If you found another issue specifically in steam, please post another answer, it can help other people!