Unfortunately, what you are trying to do simply is not possible.
A roku stick (or any other hdmi based device) is not compatible with your older tv.
That hdmi port on the cable box is an output only, meant to connect to a hdmi capable tv.
It won't work as an input or to connect to any other device except for a tv.
There are other options here, but you'd have to buy an analog capable roku model, which are now discontinued and expensive because of it. You may be better off just buying a new tv at this point. You can get a brand new 32" flatscreen tv for $200 these days. I can recommend some tvs for you, or the other roku model (though they can cost nearly as much as a new tv).
Let me know.
I am an independent technician and I've spent my personal time, unpaid, in an effort to assist with the question for which you solicited my services. This site works on the honor system, and to that end, I have prioritized working with you ahead of other paying customers.
Although you’ve already paid your fee to the site, I am only compensated for my efforts when customers such as yourself leave positive feedback for my work. Again I apologize there is not a better outcome here, though this is really beyond either of our control. I do hope you’ll consider leaving a 5 star rating for me, rather than “shoot the messenger”, so that I may get credit for my time spent in good faith to answer your question accurately.