I first want to point out that this is by and large the biggest problem in terms of time wasted that I have ever dealt with in my career. (Over two days straight now with e
This is the message that is key to understanding the issue. It indicates that Spring is failing to initialise correctly:
SEVERE: Spring context lookup failed, skipping spring component provider initialization.
(On a side note: because Spring is failing to initialise, the only JSR-330 implementation to try and resolve the @Inject is HK2 - which is why you're seeing the other issue).
Anyway, the problem is likely that your container isn't performing a scan for the annotations that make all the jersey-spring3 magic happen.
This behaviour is part of the Servlet 3.0 Specification (JSR-33, Section 1.6.2), so you should double check that your container supports this.
In the case of Tomcat - unless you're running Tomcat 7.0.29 or newer, you'll actually need to make sure that the Servlet version is specified in your web.xml.
http://tomcat.apache.org/tomcat-7.0-doc/changelog.html#Tomcat_7.0.29_(markt)
I hit this problem recently and it drove me nuts, and fixing the web.xml was easier than upgrading from Ubuntu/Precise!
Hope this helps!