I was in this position last year so I'll chime in:
HR exists to screen out job applicants, not find good ones. For example, my lab supervisor in undergrad complained that one time she actually had to contact HR herself to get them to forward her the application of a person she wanted to hire because they had decided to throw it away without even notifying the lab they had an application. When you have to go through HR for a job application your chances of getting the job diminish tremendously. That said, I eventually got my current job by applying through HR so it's not impossible, just a lot less ideal than getting in contact with a PI directly.
Anyway, HR departments have a whole bunch of different statuses that all sound the same. Things like "in review", "under consideration", "forwarded to hiring manager", etc. Each one means something different. Typically it goes "you've submitted your application" > "your application is actually being looked at by a human to see if we even want to bother with continuing" > "your application was found to meet the bare minimum standards, now we're actually looking at it for real" > "this time we actually sent it to the person who's doing the actual hiring". So keep that in mind.
From my experience, hiring decisions take time. True, sometimes you won't ever hear back about whether you got rejected or not (I had several jobs I applied to that only bothered to tell me I didn't get the job four months after I had applied). However, keep in mind that often positions will stay open for awhile and only get removed from the site when the lab starts reviewing applicants. In the case of the job I got, for example, I applied, heard nothing back, the job got de-listed, and then a month later after I had completely forgotten I had applied to that job I got an email saying the PI wanted to do a phone interview with me. The funny thing is that after I was hired the PI admitted that while they had had 40 other applications I had been the only one they seriously considered.
So don't lose hope yet, but don't expect to get hired either. It took me seven months to find a job as a lab tech, and I had excellent research experience, grades, and references, as well as a small network of contacts that gave me several leads that all fizzled out. It's really competitive out there right now.
