Bend in pipes vs clog - now what?

Argh-

Trying to snake a nondraining bathroom sink. Used a 25' hand auger yesterday - did not get far. Purchased a 20' auger today to connect to my drill - getting further, but when I encounter resistance, most of what I get is the snake kinking on me and pinching my gloves. I'm snaking for second time - I believe I got the snake all the way through before, but boiling water just rose in the sink to meet me and laugh at my efforts.

So...
1. Tips for getting the kinks out/not making it kink (I've got very little slack in the snake, but even that isn't helping half the time)
2. When I do hit something, how can I tell if it's a bend in the pipe, or just galvanized rust/debris vs. a clog?

I've pulled nothing out, so I'm not sure what's stopping it up - it's always built up to a slow drain, but usually plunging works it out. ANY tips will help - funds are quite limited right now, so calling in help is not my first option if it can be helped. I also don't know if HD will take a return of a used snake, even if I clean it up.

If the drains are galvanized, it might be a losing battle...the rust can be quite rough, allowing things to build up since it doesn't flow well. Reaming out the interior is tough, too. Plan to replace the lines when you can afford it.

Cost?

Any idea what that would run, assuming the pipe runs under the floor directly to the stack somehow (nothing else is backing up) - maybe 25" of pipe? Is that a DIY job, assuming I don't mind cutting up my floor?

Too many variables to even guess at the cost. Breaking concrete is not out of the realm of possibilities, but I would suggest that a professional concrete cutting company could be money well spent. The cut would be clean, there would be virtually no dust, they would deal with debris removal, and they would be a lot faster that you. Sometimes the least expensive way in the long run costs more in the short run. You might want to get a professional plumber with professional equipment to clear the drain before undertaking the expense of replacing it. Hand snakes often are just too small to do the job.

drain

Tub, shower, and lavatory drains usually run to the toilet pipe, which is almost always less than 25' away.