yes, that's exactly the camera i was talking about. And, yes, the 2nd link you provided shows the exact same camera and lens.
Here's the canon 50mm f/1.8 lens i was talking about (from b&h, a very reputable company for ordering camera equipment):
http://www.bhphotovideo.com/c/product/12142-usa/canon_2514a002_normal_ef_50mm_f_1_8.html
actually, if you're going to be ordering from b&h, here's their link to the canon rebel t1i:
http://www.bhphotovideo.com/c/product/613613-reg/canon_3818b002_eos_rebel_t1i_digital.html
i looked at your basketball pictures, and it looks like a pretty small gym with only 4 rows of bleachers. With the 50mm lens, you should be able to get very good pictures when the action is on your side, near the key / basket.
Also, i'm not sure if you're familiar with lenses, but this 50mm lens is a "prime lens", meaning that it doesn't zoom. So any basketball action that takes place right in front of you might be too close for this lens. Certainly, any action that's on the other side of the court will probably be too far for this lens, as well. However, the advantage of this lens is that it works great in low-light situations.
Again, i'm only making these suggestions based on your requirement for a cheap dslr system. There are plenty of options for better low-light lenses (aka. "fast lenses"). As ukcatfan mentioned, you can save up for the 70-200mm f/2.8 lens, which zooms and is great for low-light / sports, but will set you back $1,949 for the best one from canon. Sigma, a 3rd party, makes lenses that fit canon dslrs, and they have a 70-200mm f/2.8 lens for $799. So that's the price range you'd be looking at for low-light zoom lenses.
I don't have kids' basketball pictures, but i do have some harlem globetrotters pictures when they came to town last year. I used a 100mm f/2.0 lens for these photos. Hope your kid's basketball games aren't like these!

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btw, i also agree with ukcatfan's megapixel comment. You probably don't need 14+ megapixels. In reality, 10-12 megapixels is more than enough for a dslr. They just keep cramming more and more megapixels into camera sensors these days.
And i also agree that your blurry zoomed shots are likely because you had a slow shutter speed. Typically, point-and-shoot cameras and mega-zoom bridge cameras don't have a constant maximum aperture when you zoom. So when you zoom in a lot, the aperture gets smaller, and the camera compensates for this by giving you a slower shutter speed. This might not be a big deal for outside, daytime pictures because even the "slower" shutter speeds for daytime are still pretty fast. But for night time and low-light photography, it makes a huge difference. That's probably why your zoomed-in pictures appear blurry.