I need a dual zone thermoelectric wine cooler for my home. Can anyone suggest a good quality brand that can hold up to 20 bottles?

I don't know but if I needed to find out I would look first at the brands used by commercial establishments that buy for long life and reliability.

While it is fashionable for wine to be overcooled, my father's words often come back to me, "if a drink has to be chilled to taste good, it is poor quality".
White wines and pale beers are traditionally kept in a cellar.
Cellar temperatures are between 45 and 54 F; comparatively mild temperatures that for most of the year in the temperate regions no refrigeration is needed...

Koldfront 12 Bottle Stainless Steel Slim-Fit Thermoelectric ...

www.amazon.com/Koldfront-Bottle-Stainless-Slim-Fit...

Amazon.com, Inc.
Rating: 3.7 - ‎42 reviews
Koldfront 12 Bottle Stainless Steel Slim-Fit Thermoelectric Wine Cooler - Black/Stainless Steel ... Item model number, TWR121SS .... the fridge. so you hvae to take out a wine bottle to reach it an usually I would like the controls on the door and only turn in .... The door can be reversed which the description did not mention.

Koldfront 12 Bottle Stainless Steel Slim-Fit Thermoelectric ...

www.edgestar.com/Koldfront-12-Bottle-Stainless-Steel-Slim-Fit-Thermo...

Koldfront 12 Bottle Stainless Steel Slim-Fit Wine Cooler Primary Image ... steel, the Koldfront 12 Bottle Slim-Fit Thermoelectric Wine Cooler (TWR121SS) is ... cabinet and stainless steel accents ensure that this freestanding unit will look ... Power: 70 W/0.95 A .... Unfortunately, your browser does not support video elements.

Koldfront 12 Bottle Stainless Steel Slim-Fit Thermoelectric ...

www.walmart.com/.../Koldfront-12-Bottle-Stainless-Steel-Slim-F...

Walmart
$109.99 - ‎In stock

Usually with thermoelectrics they either work or they dont. Not easily repairable unless you are a competent technician as the components need metering. Sounds like a heater element gone.

Single zone wine coolers have one temperature control and the storage space is undivided so the whole cooler is at the same temperature.

You should get a countertop cooling fridge. They are very compact, about the same size as a microwave oven, and can hold up to 20 bottles of wine.

You will be spoilt for choice. There are so many thermoelectric coolers to choose from. I found a few well-known brands for you to browse through.

http://www.nextag.com/thermoelectric-wine-cooler/compare-html

http://www.amazon.com/NewAir-AW280E-Bottle-Thermoelectric-Cooler/dp/B001DI5ALW

http://www.overstock.com/Home-Garden/Stylish-12-bottle-ThermoElectric-Wine-Cooler/3105151/product.html

I had the same issue on a Whynter WC28S SNO 28 Bottle Wine Cooler, it even seems like most of the thermoelectric wine coolers, fridges, and such have the same boards by hanny. For cross refference parts I used NTE because Fry's Electronics had them.
Switching transistors - NTE51
1N 4007 - NTE125
Silicon Dual Power Rectifier - NTE6090

Also I have a venotemp wine cooler that has pretty much the same board, with the same plugs for fans, light, control panal, and cooler fan for $45 shipped at their site under replacement parts. Hope this helps people looking for info on this. Also research Switching Power Supply issues for information.

relay may be bad to compressor.does it run for few seconds and click off?