Maybe you have not set up your browser correctly. In your browser check you have ticked the socks 5 box. If you want to persist then try adding your browser name into the google search box. e.g "ssh tunnel putty firefox" and the first result from thinkhole.org does it in pictures .
When you say you want to connect to the web securely then of course you do that by entering https:// in the url instead of http://
If you mean that you want to mask your IP then say so. DreamHost is primarily a web-hosting service which happens to offer customers SSH active accounts, they probably would not be happy about customers tunneling all over the place like fevered moles. Maybe they are slowly turning this feature off across their servers.
Or, it may be your firewall and/or ISP preventing the tunnel connecting or you just messed things up.
I personally would not take the risk of doing something to upset DreamHost and risk losing your account. There are plenty of paid proxy services you can use and even a few free ones.
I suppose what I am saying is that whilst it may be technically possible to do it, it is probably not the practical thing to do no matter how honest the intentions may be.
Opinions are my own views, not DreamHosts'.
I am NOT a DreamHost employee OK! :@
Act on my advice at your own risk!