I'm not sure where you are working, but there are job shortages all over my area (upstate NY). In my hospital, one of the most successful in the area and a Magnet facility, is hiring new graduates into specialty areas! The average age of nurses these days is fast approaching retirement age so the job opportunities will just be getting better...
Next time file an incident report re: the lack of alarms for the pts. immediately. This should have a date and time on it. Be sure to detail your attempts to find one. Ultimately, maybe a short ambulation and back to bed would have been safer, but it still should be noted in the chart or incident report that the pt's exercise needs were not being met due to a lack of equipment. You may have been able to call the supervisor re: alarms available on a different floor/unit. You are a scapegoat for a system-wide problem. Your immediate supervisor should be more pro-active for her staff as well as the patients assigned there, but good luck with that! Good luck to you, dear.
I'm not sure where you are located, but at my hospital, RNs with Associates Degrees are getting hired, some even into specialty areas! You have to commit to begin your further education within 5 years, but you are already ahead of that game. I agree with the others - once you have graduated and pass your boards, you will find success. Good luck!