Under current conditions liquid flowing water at the martian surface is indeed extremely unlikely, if not next to impossible. The atmospheric pressure is so low that for water the boiling point comes so close to the freezing point that there's next to no difference. The temperature is also so low that the only place water on the surface can become liquid at all would be at the equator during high summer.
Ancient Mars, however, did have an atmosphere that was (far) more dense, so that the boiling point of water would have been a lot higher, making liquid surface water quite possible, even if the pressure would have been as low as ,say, tip-of-mount-everest.
The planet itself would also have been a bit warmer than it is now, as the atmosphere would still have contained a fair amount of the greenhouse gases, including quite a bit of methane. So the atmosphere would have retained more of the sun's energy than it does now, and would definitely have contained quite a bit of the radiant heat of the surface, which was geologically quite active at the time.
The question is whether there was *enough* liquid water on Mars to create the high pressure + heat + chemicals environment needed to kickstart "life" , and whether this environment lasted long enough to allow for evolution of sufficient complexity to allow for adaptation and survival, so that any organism that could have existed would have had a chance to leave enough of a mark on the planet for us to actually see.
For Earth, the fossil evidence shows that the earliest bacteria were already around at 3.5*10^9, give or take a couple 10's of million, years ago. *If* there was sufficient liquid water on Mars to form anything like an ocean, the circumstances there would have been not unlike those on earth. For those very early lifeforms, they would probably have been quite similar, as they were chemotrophes, and not dependent on sunlight at all.