Job Search Question?

Hello! Okay, so I've been trying to get a job as a CNA in one of the 3 major hospital systems in my area for the last 4 months or so...There is no phone number available to call HR about job openings, and it seems that the general idea is they want us to apply online where the job openings are posted. I have been doing that (no, really, I must have submitted at least 30-40 resumes since January) to no avail.
Occasionally I will get a "your app has been routed to hiring manager for further review" message, but ultimately every position I've applied for has ended up as "canceled," "closed," or "filled" (or remained in the "pre-screening" phase).

I spoke to a nurse at a hospital yesterday (my husband was having ACL surgery so I had LOTS of time to kill between the pre-op, surgery and PACU) and she suggested that I make myself "up" (you know, look nice), print out a handful of resumes, and go around to the area hospitals and literally hand-deliver myself and my resume to each unit. She said that's the best (and probably only) way to make myself stand out these days since most apps come in via internet.

What do you guys think about this? I start my nursing school clinicals in the fall, and I'd REALLY like some experience before hand (so I can get rid of some of my nerves). Also, I have heard that it will help my job search as a new grad to have hospital CNA experience (the more experience the better), and I know my graduation date will be here before I know it so I'm hoping to give myself the best odds for quick hiring after graduation. Thanks a lot for any advice you guys can give me, I hope you all have a great day!!
I've been trying to get a CNA job as a side job, and I tried contacting a few hospitals using non-traditional routes - calling, etc and they always say the application process is online. Even at the school I attend, the hospitals come in for job fairs, but just refer people to go online. One thing I wish is that they could at least send rejection letters, even if only via email, because some of them seem to be open after months, and its hard to tell if the job is still a possibility or not.

I would go for it!! That is exactly what I did to get my job as an RN. After applying for 2 months and feeling like I was getting no where I printed out my resume & cover letter, got in my car and drove around. I was intimidated and questioned whether or not this was a good idea, but ultimately it helped me land my job. I walked in and asked to speak with the nurse recruiter at a hospital I had never had clinical at. She was very nice and informative. She gave me info on how to improve my cover letter & resume and when they would be able to hire next. I had one interview there and didn't get the position. I was bummed and another month went by. Then she called me to let me know she had forwarded my info to another manager who was hiring. I interviewed and got the position three weeks later. Now I must mention this is only a summary of what my job search was like. There were multiple e-mails, phone calls and resumes/cover letters that I personally dropped off which I got no response or a "we need experience" response from. Don't give up!! It takes time!! I think it is very smart to get CNA experience before becoming an RN. I did not and still to this day wish I had. Good luck!!! Hang in there!!