Are you saying you're dissatisfied with the T3 already, or the T3 has made you realize that you're dissatisfied with your point-and-shoot?
"What DSLR would you recommend a beginner" is a huge can of worms. Most photographers hate this question.
Rule of thumb is that you should purchase:
a) What you can afford/within your budget
b) What feels good in your hand in the store
Go to a legitimate camera store and ask to try out some budget DSLRs. Pick the ones you think feel the best; ie. the buttons and controls feel naturally placed to you; it's a good weight, it's not awkward, etc. Once you have that comfort aspect down pat, figure out what the differences are between them. Generally speaking, at particular price points, all of the major camera manufacturers have competing options that are all technically on the same level. Subtle differences here and there tend to sway people one way or the other, but if you don't understand these differences, you needn't worry about them. And you will NEVER truly understand such subtle differences between camera models until you have actually shot with the cameras and learned about their functionality (and how to use a camera in general) for a substantial period of time. That said, if you want to "play it safe," go with Canon or Nikon, merely because the amount of support and range/availability of lenses and other accessories for them is the largest. Certainly other camera systems/brands can give you perhaps better value, but if you don't necessarily understand the differences between the systems, you could end up biting yourself in the bottom.
So buy what you can afford, and what feels good. Learn through experience, then worry about nitpicking later.
Alright thanks for the advice. I simply used the T3 for about a week to see the difference with a DSLR and P&S. I really liked the feel and features, and now, since I've returned it, it really feels awkward using the Coolpix L110.