As an amateur gardener: while my limited hydroponics system uses a solar pump, using gravity feeds and screws would work. You only actually need to get the water to the top of the system a couple of times a day.
I'd wonder about the process by which a "purely" hydroponics system would get nutrients, though. Composting something out that would be chemically suitable as plant food and water soluble is probably complicated. (I buy mine in a jug at the store…)
Perhaps a more reasonable system might be raised bed gardening using tiers of soil with drip irrigation or clay pipes? (Saturating clay pipes underground leaches sufficient water into the soil through osmosis without as much evaporation as surface watering.)
There are great examples of tiering like this. I love the system where square planters are stacked at 45° rotation on each tier, leaving triangles for planting — you can load those up with, say, spinach or cabbages and stack them practically as high as you like, a couple of feet apart. Root vegetables can grow in trays stacked with a little more clearance.
One can pack in production by interplanting (pumpkins below, corn stalks with pea vines climbing them), layering them (squash vines tied overhead, spinach pots beneath them, watermelon vines down below) and the like.
Given access to New World and Far Eastern plants and an understanding of which plants "go together" (eg, don't over compete for the same nutrients), there really isn't much that a Victory Garden (Americanism for "home/personal vegetable garden") uses that requires much modern technology. The main production advantages at a small scale that we have over medieval farmers are consistent access to water (plants grow more "optimistic" when routinely watered as opposed to relying on weather) and being able to Google for what-goes-where.
If you're concerned more about sheer survival than variety in cooking, a few core crops (eg, potatoes, soy, rice, or amaranth as a protein base, with a selection of specific vegetables or fruits for minor nutrients, say, oranges, carrots, spinach) can be chosen to sustain a population on very little roof/balcony space. Supplementing those with medicinal/augmentation herbs (garlic, aloe, chillies, chamomile) wouldn't be too difficult.
If you want a less Vegan populace, rat, squirrel, rabbit, quail, peafowl, and chickens are all subject to being raised in inhumane stacked warrens and fed things that are indigestible by humans.
Also, there are many mushrooms that are edible and nutritious, and could be farmed indoors/in basements.
Of course, if this is European, so you'd have the problem of cold winters and food storage as well…