Why is Chrome sending me to the Google homepage when I try to search?

Given the URL you posted, it might be related to the Instant Search feature of Chrome. It doesn't work for me and, according to some web searches about it, others.

Toggle the preference and see what happens.

In case you have a corrupted preferences file (you could test this with a pristine Chrome profile by specifying the --user-data-dir command line parameter), this should cause Chrome to overwrite it.

I created a "new" custom search engine using the below url. It allowed me to maintain the predictive search, but made the omnibox search work again (this issue is back as of yesterday, 06/16/14, for me).

https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&es_th=1&ie=UTF-8#q=%s

This was happening to me and for some reason disabling "User-Agent Switcher for Chrome" resolved the issue.

Like the answer from Daniel Back already said, it's an problem with the suggest feature. You can fix this with going to:

chrome://flags

and set the "#answers-in-suggest" flag to activate.