This is probably more appropriate for the Cathay Pacific or oneworld forum, but since you're here, I'll take a shot.

I've flown this route (or parts of it) several times using CX. The problem is that (in general) CX only operates 1 turnaround flight a day from HKG to DPS and back to HKG. Unfortunately, the return flight mis-connects with all of the North America departures in HKG (except the late flight to YVR), meaning you have to layover until the following day.

Schedule and fares are below:

Outbound
JFK-DPS (everyday)
CX889 JFK 20:40 HKG 06:30+2
CX785 HKG 09:55+2 DPS 14:40+2

Return
DPS-JFK (everyday w/layover in HKG)
CX784 DPS 16:05 HKG 20:50
CX888 HKG 14:25+1 JFK 18:50+1

Fares are as follows:

Y (discount): $1,118.96
Y (full fare): $4,364.96
J: $6,564.96
F: $10,780.96 (only J service HKG-DPS-HKG)

On Fridays and Sundays, CX operates a morning DPS departure that arrives 20 minutes before the JFK departure from HKG; unforunately this is not an allowable connection (not enough time). You would, however, be able to connect to the 2nd YVR flight of the day, and then fly AA from YVR to LGA (or EWR) via DFW. This schedule is below:

DPS-JFK (Friday & Sunday only)
CX786 DPS 09:15 HKG 14:00
CX838 HKG 16:40 YVR 11:55
AA330 YVR 13:30 DFW 19:34
AA778 DFW 20:46 LGA 01:01+1

Fares [i]should[/i} be the same. If you plan on flying J or F, you can probably do this trip cheaper on a 1world explorer around the world ticket.

QF also serves DPS from the U.S. via multiple transit points in Australia, but this would be much longer and (I believe) more expensive.