Steam problems, can't update, whatever the case, you can try these steps out.
If you can't update or login to Steam, try these. These are the main solutions that has managed to get Steam working for different people.
Solution #1
This is the most famous one, which is to delete ClientRegistry.blob in your Steam folder and run Steam for it to update. You should always try this first.
Solution #2
Download an updated version of Steam here, then extract it to your Steam folder. Try and update after that. This helps if your Steam update doesn't complete because it is too slow, or something of the sort.
Solution #3
If you have connectivity issues, try disabling your firewall. There are some programs that conflict with Steam, making it unable to connect or update. For example, if you have DAEMON Tools or Advanced System Care, you can try exiting it.
You can see the list of conflicting programs here.
Solution #4
The number one solution for Malaysians because of their ISP. You can try this too if all else fails. Download Hotspot Shield, install it and connect to the Hotspot Shield server. Try running Steam and see if it works. You can disconnect and exit Hotspot Shield after you've connected to Steam, because Hotspot Shield sucks in a way.
If all of the solutions here didn't work, you can pretty much say Steam sucks.
Love,
Nicholas.