what is the weakest link in my audio chain

There's lots of ways you could go about changing your sound. Not knowing your acoustics and setup, changing speakers yields the most dramatic change in the electronics chain. Yes, upgrading wires is a cheap (sometimes) way to tweak your sound. That said, I'd dump the HD power cord you're using as wire, and go with HD sprinkler wire, for an imediate improvement, yes! (best sounding stuff at HD for wire, hands down!).
Still, at this point, if you are not planning a speaker swap(try-out), I'd upgrade the Bryston, as it's just an "OK" sounding amp, not so much top end, not so refined throughout, and a bit warm/fat sounding. It's same as Lexicon amp basically. Others to consider would even be Classe, Parasound, Anthem, Aragon, Krell's ok, McCormack, and other's you could try.
The pre/pro you could and should upgrade to something with newest HD codec's, and latest DSP room correction, yes, like the Audyssey processing, for superb acoustical benefits to the sound of your system.
Interconnects, I'd be defaulting to harmonic Tech Truth Link. Very neutral, clear, good detail, good dynamics, well balanced - better than the Outlaw, for $100/pr used.
And, yes, there's better speaker wires you can chose for more.
AS for your speakers, the NHT line offers some sonically more neutral, clearer, even more extended (if accurate) sounding speakers, with good dynamics. Also, the Dappolito configured speakers are nice and dynamic and strong through the upper bass midrange area, as well as re-inforcing the treble with the right crossover, for a stronger pressentation for movies and dynamic music, with better integration into a room, acoustically (less ceiling to floor reflection issues, for better detail and more solid image - all things considered. Again, I don't know your room/setup). Speakers like NHT's M5's make excellent music/ht monitors, for passive speakers for cheap. That of course, is if you're planning on experimenting with better speakers - and I would, if I were you.
In the budget speaker realm, there's lots to chose from, of course. It just must all balance with your setup, your system, your tastes, and life-style. (your Paradigms are a more traditional stereo speaker, with tweeter on top, which interacts with the ceiling more, which is not usually a strong HT/music speaker choice, with challenging acoustical issues) I would look for dual mid/woofer designs, really.
Speakers like Thiel SCS4's are more refined yet, but not as strong dynamically in a larger spacel, and they're more money.
At any rate, you need to experiment with ONE VARIABLE AT A TIME to really know what you have going on in your system, at any point. So concider. (it's a hobby if you want the most out of it....unless you get REAL REAL lucky with the first shot or two)
good luck

Yeah, try swaping out that HD power cord you're using for speaker wires with one run of adequate length 11 conductor sprinkler wire, or two lengths per side of 7 conductor, and see what you think! Then YOU'LL know. Good luck

I don't think I ever remember ANY Paradigm speaker I ever sold, EVER sounding bright, from my recollection. Infact, I think they're a little shy in the treble from what I remember.
And the Bryston should keep the sound mellow.
I like a little more extended amp with those speakers, really. But, experiences vary.
Personally, I think people here some setup somewhere, where they hear some tonal character, and they make assumptions! Can't tell you how many times over the years I've heard bad combo's of gear, only to have people make assumptions about one piece of equipment in the chain - as if the sound was coming from only that specific component!
Um, no, the paradigms were never bright. Infact, I dare anyone to find any reviews that describes a paradigm speaker as having a bright ANYTHING!

"I tried a few dealers but none of them was willing to let me bring an item home for audition, even though i promissed that if I like the item I will buy it." (Benqsun)

Alright here's a little insight from someone who's worked in a few high end audio stores over the years.
I think what you're experiencing is that retailers have learned over the decades, that home auditions are about 95% BOOMERANGS! Auditions, with no strings attached, DO NOT work! - And the product is MOST ALWAYS destined to come back to the store. Why? Because any audio enthusiasts who's interested in experimenting with his system, will continue to do just that! - EXPERIMENT! And he'll be on to the next line of products he's considering to see what else is out there. That IS the way it happens, regardless of what any customer may tell you up front.
Why would someone running a business, that's already extremely difficult to keep profitable, offer a "try-out service" for his products? Time is money, and that's money well wasted basically. These types of customers (audiophiles and audio/video enthusiasts, alike), from my direct personal experience, are largely curious, uncommitted at that point(I mean they want to try the product because they're uncertain about ALL their options), and simply running a "science project from the library", basically! These are not the kinds of customers that will pay your bills, trust me!
That said, I ask you, "would you loan equipment out to people you KNEW were not going to buy anyway?" If you answered yes to that, you might wanna consider another source of income. Believe me!

"They insisted that I buy one and if not satisfied, take it back for an exchange for better (more expensive) ones."

Andrew Singer, from Sound by Singer on the East Coast US has been using this approach for years. And he's been one of the very very few ultra high end audio salons that has mad it work! He's no dummy when it comes to making a sale, and getting products to the customers. I can tell you that much. He understands that if you simply let the customers, say, borrow your Porsche for a week - to have fun with - and you don't make them commit to buy one model or another if he let's them borrow the car (so to speak), they will return the Porsche with a simple "thank you", and be on their merry way!...not only that, but leaving you left having to clean the sucker, and fill in all the dents and scratches, when you're done having your jollies with it!

Business is business, basically. You can't let kids run through your store, unrestrained, and hope to make a profit! If anyone is interested in doing a "trial run" on some gear, and tinkering like an audiophile, they can EASILY buy ANYTHING AND EVERYTHING - for cheaper, mind you - over the internet!
Just don't expect your local mom-and-pop high end AV store to offer a "try-out service", a "loaner program", a 30 day (Best Buy), no questions asked, return policy (after you figured you really need the rent money, or your wife says she would rather to go on a vacation with that money instead) and expect to be in business the following year.