Well, I would at least open the access point to see what side of the blockage you are on. Grease is a big problem with kitchen drains. Make sure you aren't putting grease down there...

Then, yeah an auger is about the only way to go AFAIK.

__________________
1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra