What to upgrade next.


This is my first foray into the forum other than reading other's post. I hope respondents will be kind! I am at the very low end of audiophile equipment and many of you may not think I am there yet when I list my equipment. The economy has become better for myself and I am looking to upgrade but not exactly sure where to go from here. I am sure I will receive many different suggestions so I plan on taking the one suggestion that I receive the most and employing it. My equipment is as follows: Denon AVRx 3500H as my integrated amp which is boosted by a Bob Carver Cinema Grand 5 which pushes 200wpc. This powers my Polk Audio RTiA7's which are my music floorstanders. When I started upgrading I chose the Polk's as they seem to punch above their weight. After months on this site I am unaware of many people who extol the virtues of the Polks so I am thinking this may receive the most as far as recommendations. I stream most of my music from my desktop and laptop. The desktop sounds like an airplane waiting to take off. I am not independently wealthy but am looking to spend between 2-3 thousand if necessary. The one thing that gives me the biggest headache at this point is music delivery as computers have glitches and my angina acts up when the music cuts out in the middle of Alex Lifeson shredding his axe. My music files range from bad copies of MP3s which are slowly being replaced to HD Audio files. Thank you for any suggestions.
dadork
Since you like both music and movies you could keep what you have and perhaps try different speakers, get a streamer like people have mentioned.

You could also look at a preamp with Home Theater bypass. I have a full home theater setup for movies but like music just as much. I was considering getting a additional system just for 2 channel music but another option would be a preamp with HT bypass. That way I can combine both systems.

If you are able you might try connecting your receiver and computer via network cable and then try your music through HEOS, you might notice a improvement in sound quality.

Also I would personally try one new component at a time, that way you will be able to see how much of a difference it makes. That is a little hard to do when adding 2-3 new items at a time.

Will
At least start with the 2i. It has a serviceable DAC aboard that you can play it through until you can upgrade. They are $549 plus tax. You can put whatever files you have on a USB flash drive or SSD and play 'em on it.  You will find the sound and control via their app on your phone to be far superior to PC sound. Down the road you can shop for amp/speaker synergy.
Many preamps (and integrateds) now have HT (home theater) pass through so you can keep the avr for surround video.
Good luck.
Thanks @fuzztone. This seems to be the consensus as far as the streamer. This step will leave some meat on the bone as far as the money goes and I can wait a bit to get something much better in the pre-amp or speaker department which is what I think I am weak in right now. I suppose I should have mentioned in the OP that I am using a sub and it too I think a weak link. I am using a Klipsch 10" ABC Warehouse special.
@flrun Wouldn't Zone 2 setting be considered a pre-amp bypass? I am definitely committed now to getting the streamer as I think I am getting a clearer view of what it is and does. I should have mentioned in the OP that I am running 2.1 and 5.1 with my sub as another weak spot. It is an ABC Warehouse Klipsch 10" . Thanks for your help!
Dadork,
You may consider the route I took, buy use. I have 6 systems, 5 of which I listen to on a regular basis.  Other than the one I bought in 1984 all equipment was bought used. I enjoy all of them , some more than others. All told I have less than your  budget invested ( not counting the 1984 purchase ) I suggest that you use a good streaming service ( Qubuz,  Deezer, Tidal ) and as already mentioned, improve your internet. A wired connection sounds the best to me.
My up grades would be a better streamer & dac ( currently a Yamaha WXC-50 ) & room treatment .