There are two parts I want to discuss.
Part 1:
I think you may have unrealistic expectations. There is little out there which is going to sound much better/worse than what you were using before. A/V receivers have a job to decode digital audio, which most do reasonably well. Some higher priced ones do a fair bit better, but those are models well outside of your budget, so hardly matter. At your budget, you have an extensive list of models which will work just fine, but not sound one bit better.
Why?
Because your speakers suck.
Don't shoot the messenger, but Onkyo produces great packages for the money. You get a lot of value there, but you don't get a lot of quality in the speakers. The receivers tend to be decent (see part 2 below), but the speakers tend to be very low quality. I wouldn't avoid their receivers at all, and, in fact, I would recommend them at your budget because you have other, far more important needs, than a new receiver.
You need speakers. I would strongly suggest you go speaker shopping. Listen to different models within your budget, starting with left/right mains, and adding a center if you can swing it, then consider some surround speakers. But, you need speakers if you want an improvement in sound quality. I can tell you first hand what I experienced, and what others will echo. When I bought my first home theater in a box (HTiB) kit, a Kenwood system, I was happy. But, I felt like you that something was lacking, so I went out and bought $1,000 in speakers (a great deal at the time), and a $2,800 A/V receiver. Well, the speakers showed up first. What the heck! I gotta try them out, so I pull the Kenwood speakers out of the mix and I plug in my new Def-Tech BP30 speakers, and the sound difference was astounding. Flat out, amazing how much difference there was between the cheap speakers and the good speakers on the same A/V receiver. The details that I was missing was suddenly present. Not only was it cleaner sound, but it played far louder than the smaller/cheaper speakers could at the same volume level. It was just a much more efficient design. When I received my $2,800 receiver a few weeks later, I was psyched, but really, the nice receiver offered almost zero improvement at normal listening levels. It was not the receiver which was creating the sound, it was just delivering the power. It is the speakers which deliver the sound, the speakers which matter, and the speakers which ultimately are what disappoint many people.
Now, if you want to 'crank' your system, there is no A/V receiver in your price range which will deliver. Cheaper products like this have smaller amps that overheat more easily and shut down more readily. Even receivers up to $1,000 new have this issue. About the only way I've seen systems crank out power without thermal overload, for hours on end, is with external dedicated amplifiers. That gets into some pricey systems, but it allows you to crank it for hour after hour without system shutdown. So, any receiver in your price range is going to handle more reasonable sound levels for long periods of time.
I would recommend you pick something up from Accessories4Less...
Home Theater Receivers | Accessories4less
No specific model is going to be worlds better than others. Denon and Yamaha are models I prefer, but they will still go into thermal shutdown if driven to hard.
If you DO want to have the capability of adding an external amplifier to drive things at some point, then you must get a receiver which has 7.1 preouts on it. If you look at the back of this model, you can see that it has this feature (bottom center)...
MARANTZ SR5005 100w X 7ch 3-D Home Theater Surround Receiver | Accessories4less
Most cheaper A/V receivers don't have analog 7.1 preouts on them.
There are, in fact, only two which do under $450 on the A4L website. The one listed above and this one. I would think this Yamaha may be a bit better.
YAMAHA RX-V773WA 7.2 Channel Network AV Receiver w/Wireless Adapter | Accessories4less
Part 2:
Now we have a different topic of discussion...
Why did your old receiver fail?
Did you spill water on it? Was there an electrical issue in your home? Did something else occur?
Most likely: Did you run it loud and have it in a tight space?
The first options are perhaps once-in-a-lifetime events. Sucks, but it happens. I lost a TV once because of a marble. I don't expect to ever have that occur again (and my kids still owe me a TV!). You also do want to consider a good power conditioner, but the last thing, that's the number one killer of electronics.
People think they can stack cable boxes and other equipment on top of their A/V receiver. They think they can put the receiver into an enclosed cabinet without ventilation. They think that just a couple of holes for ventilation is sufficient to properly cool their devices which crave cool air and open airflow.
Obviously, I'm not sure what applies to your situation, but if the reason for the failure of the Onkyo was due to running it hard, without sufficient airflow, then you need to correct that issue. It is NOT a failing on the part of the manufacturer, it is your issue. You have to run volume at levels which are reasonable to the product you have purchased, and if you want more, you have to put the money into the system to get more... if this applies to you at all.
But, it is something you want to address so that you get years of trouble-free use out of your A/V receiver.
Oh, and I sold my old Kenwood just a few years ago, still working fine, and that Yamaha which I purchased to replace it over ten years ago is still working great. So, airflow, and decent power really can keep things running (along with some luck).