I'm studying medicine now, and I couldn't imagine it without online journals, databases, and Wikipedia (oh, yes...)
We're taught that most of good patient care is about taking a good history (ie listen to the patient's story, hear what they're saying, and ask the right questions) and common sense thinking. "Don't let the tests/technology do your thinking for you" is something I hear a lot.
The technology can sometimes be a trap, just as any tool can be a trap (to a man with a hammer, everything looks like a nail). It can be tempting for a doctor to order some test or treatment because it's a usual thing to do, without a reason specific to the particular patient situation.
I don't have a lot of hospital experience, but it seems that most of the technology is in the ICU and operating theatres, and most of the devices I've seen don't do anything that can't be done manually.
In the operating theatres I spent a week in last year, for example, the anesthetist has a machine that can control ventilation and gas delivery in wonderful ways, monitor vital signs, and maintain a record of all anaesthetic events including what drugs were administered when. But, beside the machine are the simple low-tech tools that will also get the job done. Masks, bags, airways, pens and paper, oxygen. And these simple tools are used regularly - there's nothing that isn't used every day.
There are wonderful technologies that can't be replaced by low-tech methods, but as far as I know (in my limited experience) these are for special cases - they aren't essential to keep the hospital running. They make patient outcomes better than they would be without them, and if they broke, it wouldn't make outcomes any worse.
Record keeping is an interesting area, which (in the hospitals I've been in) is pretty much all paper based for day to day clinical care. That has is drawbacks, which may or may not be worse than the drawbacks of a mostly electronic system.