Get a helpdesk job at a company with an internal helpdesk. (NOT a call center). Those jobs truly are entry level, and will hire people without experience. Once you are there, start building tools on the side to help your department. If you do well, they'll see the value and give you more programming work. If not, at least you now can put real IT experience, including programming on your resume.
Admittedly, this is not an exciting path, nor a fast one. But it is an effective one.
...says the student to the 20 year veteran who lived this path.
If all you care about is startup work, yes this is bad advice. If you want a solid career in technology, this is a viable path. You don't have to agree, and I don't expect anyone to like it, but denying its viability is just short-sighted.
Admittedly, this is not an exciting path, nor a fast one. But it is an effective one.