Onkyo HT-S5400 Bass Issues

I recently upgraded to my first real stereo system. I picked up an Onkyo HT-S5400 because they make quality products and it fit my budget. I have been very happy it, except for with regards to music. Movies sound amazing; TV sounds great; music sounds like crap.
When listening to any type of music, whether it be an MP3 file on a USB drive or a CD, I get serious bass issues. Basically, 80-90% of the time, there is extremely little bass performance. For a sub this size and power, I should have killer, thumping bass. With movies, I have to turn it down because it rattles frames on the wall. With music, it just makes me frown.
I will be listening to it, and the bass will randomly cut in and start functioning as expected. Then, at some point, it will cut back out, and sound weak and muddled, like I have it turned super low. Most of the time, there is very little bass. It could be on the first song, or after listening to ten songs. I can never tell. And it might go back out at any time. I will be listening to it, and there will be nearly no bass, and suddenly, it will start thumping like it should.
I have tried messing with just about every setting available, changing listening modes, and everything. I have the receiver set up just how I like it, with the sound I like for my room. But I just can't get bass to perform properly with music.
Unless there is some sort of magic setting I am missing, there has to be some sort of other issue. What could cause this? I know it's not just that the sub sucks, because it doesn't. It only sucks with music, and only most of the time. But those other times, it will kick in and really start kicking it out. I mean, this is not an amazing high-end system, but it should sound good.
Any ideas?

I have tried changing sound modes (stereo, all-channel stereo), changing listening modes, adjusting receiver settings, checking the connections with the sub... If there is a setting, I have tried it. What gives? The last thing I want to do is have to pack all of this up and ship it back. =-(

Well, the issue is apparent with multiple devices. Like I mentioned, this happens with files from my media streamer, or discs I play in my Blu-Ray player. However, it is only apparent with music. I have never noticed any issues while watching movies or TV. I can put in a Blu-Ray movie, and it will have thunderous, shaking bass. Then I put in a CD, and it sounds like crap.

All of my connections are HDMI. I have a TV, the stereo, two media streamers, and a cable box. I have tested music on an external hard drive, USB stick, streamed from PC, and on disc. All of the cables are solid and seem to be working fine.

I would blame the EQ on the stereo, but like I said, I have tried just about every setting. Nothing seems to change this problem, and I don't have it with other types of media.

The BD is LG. The TV is LG as well. I have the music EQ set to "Rock," because it seems to fit the sound of my music best, but I have tried all settings, just in case that was the issue.
I ordered a new, higher-quality subwoofer cable that I am waiting on now. I am going to try replacing this one with that one, and moving the subwoofer to a separate outlet on its own surge suppressor.
For the HDMI cables, I would buy it if I had the same issues with other materials, but I don't. Why would I have poor bass performance on a CD, but not on a Blu-Ray disc played on the same player?

The setup is like you said, all HDMI to receiver. Nothing is going through the TV. The only exception is the media player, because I have it on an HDMI switch.

The sub is inches from the wall on each side, without any obstruction.

Yes!!! Finally, I can listen to my music. Replacing the subwoofer cable fixed the issue. The wimpy Onkyo cable just wasn't enough to carry the bass to this powerful sub I think. I replaced it with a thick, 24-carat gold-plated cable, and it worked like a charm. Thanks for all of the assistance and support guys. I appreciate it! =-) I am so happy.