Can a $750 system sound good?

Well, good no but not too bad maybe.
Used original Audiolab integrated - $250.
Some used DVD or CD player - $150.
This leaves $350 for used older speakers and cables.
Yeah, there will be some sound coming out.

Of course!  If you only spend money where it matters. 
Streamer - very marginal gains, if any at all, over a Raspberry Pi 4 plus Allo HAT.  $100. 
DAC - Khadas Tone Board. Excellent. $100. 
Any class D low distortion amp. $300. 
Van Damme cables at $4 per meter. 
Mark Audio Alpair 11MS full range drivers. $150. 
$100 left for some birch ply. 
Then get the free plans for the Frugalhorns Mk3 : https://www.frugal-horn.com

Bingo! 

Another option is to spend $700 on the best active speakers you can find, $50 on an Audioquest JitterBug, and hook them up to your laptop.

That’s a great suggestion. Although not full range could add a cheaper sub later. 

Easily. (Good =/= Great).

Any older NAD Power Envelope, T761 etc, pre-HDMI Denon receiver, locally available tube receiver, occasional bargain Carver etc. $200 - $250

Craigslist floorstanders somebody doesn't want to move. Allison 7, CV D-5, Thiel CS2, vintage Wharfedale, recent Klipsch/Polk. $200 - $500

PS3 for CDs. $50 or less. If there's money left over a Marantz DVD player or any laserdisc player ~$70 - $150.