Why can't I heat water properly on a new glass cooktop using a stainless steel pot?

One possible reason for this would be if the cooktop used induction, where rather than heating up, it used electromagnest to cause the pan to heat up. For this to work, the pan must be ferrous and able to be magnetized. Although stainless steel is made from iron, it isn't strongly magnetic, and thus will not work well on an induction cooker.

To test if this is the case, you can try pans from other materials and see if they have similar problems. Aluminium, copper, or ceramic cookware simply won't heat up at all. You can also try turning an element on high without a pan, and waiting a minute or two. If you can hold your hand above the element without feeling any heat, it's either an induction cooktop or defective.

If you place a cast iron or carbon steel pan on the element, wait another minute or two, and test again but can feel heat, then it's induction.

As you mentioned it's a new cooktop, if it's new because you bought it (and not because you've moved), find the manual, and if it's an induction cooker, it should proudly proclaim that fact, and list what types of pans are recommended.

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The next possibility is that if you're coming from a gas cooktop you may not be used to the speed of electric cookers. With a glass-topped cooker, it's difficult to see the size of the elements, and so you may only have one or two elements on the cooktop that are rated for fast boiling or other high-heat applications. You can try each of the burners in turn, and see if some of them heat up faster than others.

... but there's also a chance that the element is defective. I'd suggest calling their customer service number, or e-mailing them to ask about the cooktop.

Let me preface my answer by saying that I have a gas range, not a glass cooktop. However, I have found on both gas and electric ranges that there is a world of difference in pans made of different metals.

I have two sets of stainless steel pots and pans. One is a more expensive brand with a thick bottom and the other is a more moderately priced set with a pretty thin bottom. With pots and saucepans from either set it seems like it takes forever to get water to boil. It's very frustrating to say the least.

Also, it causes issues such as when boiling eggs. Because I put the eggs in before the water boils and start timing when the water starts to boil, I never could seem to get the time just right as the eggs have set in very hot, but not boiling, water for an extended period.

What I have found that works best and quickest for me when boiling water for eggs, pasta, etc. is porcelain enamel cookware. (This is a porcelain enamel coating on aluminun - not to be confused with enameled cast iron.)

I'm not sure if the porcelain enamel cookware is appropriate for glass cooktops. I would suggest trying cookware made of materials other than SS, always making sure that it is appropriate for use on your cooktop.