I know how frustrating it is to deal with most online application systems - especially those poorly designed ones that don't provide any feedback so you don't even know if your app went through or not! GRRR. However, I want to point out that there are a couple of major reasons that most hospitals are going this route.
There are a ton of Federal requirements impacting the employment process. Employers have to collect data on all applicants so that they can defend themselves against claims of discrimination or other employment law issues. Automated systems are the easiest and most accurate way to do this.
Currently, there is also the issue of how to cope with the enormous numbers of applications that are received for every opening. HR departments are hard-pressed to even deal with the increased work it takes to sort out 'qualified' versus 'non qualified' for each position. Automated systems can do this work for them. Of course, if they have a bad system or haven't set it up properly with the appropriate screening triggers - - it is probably not very effective.
Bottom line - if a company has an online application system, there is NO WAY to bypass it. But you can take precautions to at least make sure that your application makes its way through the electronic maze. First of all, fill in ALL the blanks - don't just type in "see attached resume" because that won't work. Double check all info to make sure there are no typos or mistakes... you don't want your app rejected because you typed in someone else's SSN or license # by mistake. If you are attaching a copy of your resume - don't use any fancy fonts or formatting because these may not be compatible - your resume may end up as a page full of undecipherable symbols. Many systems these days have some sort of built in 'screening' questions that are designed to weed out unqualified applicants... answer these questions with the job (you are applying for) in mind, but be truthful. For instance, if you state that you have 10 years of experience, but your demographic info shows that you graduated 6 months ago it will trigger a mismatch and kick out your app.
"Cleanse" your social networking footprint and make sure you have appropriate privacy settings. Employers are beginning to look at these sites for background info. You want to make sure that any discoverable information shows that you are a serious professional, not a party monster with a poor work ethic.
Finally, if you you do encounter technical problems with the online system, please take time to report it to the HR folks. They can't fix it if they don't even know that there is a problem.