My new convection/convention oven will not bake anything correctly

The first thing to do is buy an oven thermometer to see what temperature your oven actually is. Technicians have no real way of knowing what the temperature is when you are using it; what you need is hard data. Oven thermometers are very cheap, and it will give you a better idea of what's going on. Put one in your oven and then turn it to the temperature you want, then see what temperature it actually gets to.

Next, read your oven's manual thoroughly to make sure there's not something you're missing. One of my ovens wasn't working--I set the temperature and mode but it wouldn't heat. I thought it was broken before I figured out it wouldn't work if the clock's time wasn't set. Don't ask me why it was designed that way, it doesn't make sense but there it is. Some ovens have a start button and won't change the temperature unless you press it.

My suggestion is simple: return the oven. It's likely that you purchased a defective oven. Many countertop ovens have manufacturing defects, and the easy way to handle this is return-and-replace. I suggest also browsing online reviews for the model you purchase, as some countertop ovens are defective-by-design.

Not a full answer, but some steps to troubleshoot/may help:

1. Hang a manual oven thermometer in as close as possible to the place as you would normally put your food. Make sure you read it through the window without opening the oven. You may have to move your racks so that you can get the thermometer to the same height as you food would be at. Do a dry run of cooking your most basic recipe--preheat, open and close the oven exactly as you would normally, etc., just without food and keep notes of what the thermometer says (start, end, and maybe 4-6 times evenly spaced through the process). Let your oven cool completely, then same process again, but with convection mode on. If you have a friend or relative who will let you repeat the process in their oven, do that, too. (Manual thermometers are extremely cheap, so you can also get several and hang them in different places.)

2. Buy a box cake mix (yes, yes) and prepare it exactly as specified on the box, cook at exactly the time and temperature specified, etc. Weigh it before and after cooking to calculate moisture loss. Take notes about the doneness in various spots: edge, one third of the way in from the edge, center, top, and bottom. Report back here.

3. Try putting your food in a Dutch oven inside the oven, turn convection mode on. If you don't have a Dutch oven, you can put your normal dish on a cookie sheet with an oven safe bowl covering it, or you can use foil (but make sure the foil is fully encasing your food and secured so it doesn't get blown around). (It might be worthwhile to sacrifice another box cake mix here just for consistency, so you can compare the same doneness points as from step 2.)

Thoughts: Convection oven is basically the same as a normal oven+fan, but of course there are options even with normal ovens.

Normal ovens usually have a significant temperature gradient from top to bottom (hotter at the top), the fan on a convection oven distrutes the heat more evenly. If the power is the same, with the fan on it will be--compared to fan off--cooler at the top and hotter at the bottom. Since most people tend to cook closer to the middle or bottom, for most people the convection mode will be hotter (at the same power) than conventional. However, some convection ovens try to adjust the power for you based on mode, so the power might be different for the same temperature setting depending on if the fan is on or not. (This might also be a place where things can go wrong.)

The exact shape of the interior and the arrangement of the heating elements/burner can also cause hot or cold spots in an oven...you only really care about the spot your food sits at.

Some ovens also have options re: which heating elements are on (top, bottom, both). Convection ovens may have fan speed, etc., options, too. It may be worthwhile to cuddle up with the manual and list out all of the options which your oven has, then try each one from a cold oven with the temperature set the same and thermometer in the same place, note temperature as intervals that make sense for the types of recipes that you normally cook. (It can also be helpful to do this for the minimum and maximum temperatures which your oven supports, so that you know the full range actually available.)