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Some evidence
There is tons of psychophysics and neuroscience on the sensory side. To name just a few.

More generally, there is no break during evolution in the underlying computational mechanisms that support sensory representation, attention, working memory, decision-making: all the processes that seem clearly important in consciousness are there in full bloom in nonhumans (pubmed will show you the huge literature on this quickly). None of these processes popped on the scene with language (which is an idiosyncratic and weird system of communication that only 1 out of 40,000 vertebrate species evolved).

Further, the brain-stem core that supports the waking conscious state is common to all vertebrates: the thalamocortical processing stream and reticular activating system for arousal/wakefulness:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2701283/

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2962410/

This seems to be part of the machinery that is shut down when you are anesthetized:
https://www.ncbi.nlm.nih.gov/pubmed/25172271

The nice thing in animals is you can manipulate this, even recently using optogenetics you can wake mice from anesthesia by optogenetically stimulating the arousal system:
http://www.pnas.org/content/113/45/12826.abstract

Comments
I am not saying we can prove that animals have subjective experience, this is the wrong standard. In science, we don’t prove, we find what is reasonable to conclude based on the cumulative evidence and our best thinking.

Note also I realize that Dennett doesn’t think that language is necessary/sufficient for consciousness. However, his human-first, language-first, heterophenomenology-first approach is not biological, and leads him to say very strange things (like how much of a mystery it is whether nonhumans are conscious because they can’t talk). One thing to notice is that philosophers who are fond of language as a model for human brain processes tend to ignore sleep, anesthesia, dreaming, and other “mere physiological” processes. It’s because they don’t have the tools to handle them from within their linguocentric perspective.

Neuroscientists and psychologists have been tackling this stuff for decades in nonhuman model systems, looking at Dennett with bemusement while he uses a lot of words and metaphors to say a few interesting things while he contributes…not so much, but is extremely popular among nonspecialists. This is typical of philosophers: how much have philosophers contributed to the first-order development of physics, math, geology, etc the past 50 years?