As well as facing prejudice because of his disability, he also said people judged him because he is a beneficiary.
"People who are like me, who are on a benefit have a more solid income than someone with a job.
"As much as I'd like to, I can't get fired from being a disabled person."
During his flat hunt, Dempsey conducted "tests" to see what got more interest - when he mentioned his disability or when he didn't.
"I've gotten a lot more results by not telling them I'm disabled before I turn up [at a flat viewing]."
Dempsey's flatting struggles aren't unique in the capital but renting advocacy group Renters United believe when it comes to flat hunting, disabled people do have it tougher.
Organiser Robert Whitaker said the lack of supply meant landlords could be highly selective with their tenants.
"That makes it really hard for people who might not look like the traditional or easiest tenants for them, so any people with disabilities struggle, people with different ethnic backgrounds or with limited language can struggle as well to find a place."
He said biases, whether they were conscious or not, seep into people's decision-making - especially when they have a big list of people to choose from.
Wellington City councillor Rebecca Mathews, who holds the accessibility portfolio, said the country's rental market isn't very accommodating to people with disabilities.
"There's a lot of us that need to think about our attitudes to disabled people and see the strengths that disabled people bring to all aspects of life."
She said differently abled people just wanted to be treated like everyone else.
After months of couch surfing and temporary accommodation, Dempsey is relieved to finally have a place to call home, but the stress he faced locking down a flat as a disabled person remains front of mind.
"If you just keep an open mind about disabled tenants, and having one, they really are no different than anyone else applying for your flat."
