What is a direct response marketing and data analyst in terms of jobs at a tech company?

Those are code words for: data entry and telemarketing.
Direct Response means answering incoming calls (sometimes—or sometimes they REALLY stretch the truth and mean that a computer-dialer will bring incoming calls to you).
If you’re training for a computer science degree I’d look for an entry-level analyst job that directly refers to WHAT you’d need to know..
You want it to be something like: “SQL database business analyst”.
Alternately, a very good start for someone interested in working in a computer field is as a QA tester for a software company. You’ll learn a lot about what CAUSES bugs / software defects and can eventually put your coding skills to work—maybe even for the same company where you start out as a QA analyst.

Thanks for your help. I’ve been searching for some QA tester jobs but they all seem to require more experience than I have. I wondering, I’m looking for jobs where I can work for a Rails developer. I guess, an apprenticeship of sorts. Am I naive? Do these even exist nowadays?

Internships are rare for software development (because from a company’s perspective it takes so much to get you up-to-speed on their methodology before you’re productive and writing code they’d actually keep in their product) – but if you look for a larger company you might find something.
I don’t know what area of the country you’re in – but if you are fortunate enough to be in the Bay Area (Silicon Valley) there are several larger tech companies (Fortune 500 types) that still offer internships.

I broke into software development (as a second career, like you) by first doing QA – that’s why I pointed you that way. It’s a way to quickly become an “internal expert” w/ a company’s product..so once you know the product’s functionality very well it makes you a better internal candidate for a development position.
The key in s/w development is to not be proficient in just one skill (we’ll take people who’ve only ever done C+ before, for example—and make them into Java experts) but to have a particular strength. For example: performance tuning or ANT scripting. Also, database experience is pretty much required. If you aren’t already proficient in PL/SQL or SQL – time to pick that up. Anything you do (even web design) will invariably lead back to needing to make db calls—so pick up some database design experience. Also, Unix skills are never to be underestimated. I hated learning vi – but I still use it to this day. (Used it just last week in fact..) And I’m not even in development anymore.

I’m bilingual (Japanese/English) and came from a software localization background – this is (was?) a rare skill in software dev…which made it easier for me to get hired (back in the day).

So, if you can – go for a quick course in a testing methodology (some sort of QA certification) above and beyond your course work. Then you’re more likely to get your foot in the door. There are also a lot of companies that specialize in QA (so that companies can bring them in as external resources)—see if you can find one like that, mention your computer programming language skills and see where that gets you.
And, if you have the time/ability to add some language classes to your course load I’d recommend it highly. Some of our best dev architects actually came from mathematics and linguistics programs rather than a CS background. One of the most talented guys I’ve ever worked with had his undergraduate degree in Russian.