Does the brand of lense effect the picture?

I'm not the most experienced with camera lenses and unfortunately I broke my current one so I'm looking to get a new one.

I currently have a Nikon D90 with a 105mm lens (broken one) and the information is Nikon 18-105mm f/3.5-5.6. I'm looking at another with the same size: Nikon AF 35-105mm 3.5-4.5 Lens.

Is the one I have now better or the one I'm looking at?

I'm into sport photography so I don't need any macro lens, I just take photos for a hobby.

Should I just get my current lens fixed, buy the other (Nikon AF 35-105mm 3.5-4.5 Lens) or get a Nikon DX AF-S 18-135mm lens?

With any lens starting at 35mm you would have no wide-angle capability such as you had with the lens starting at 18mm. So that's the first thing to think about.

I suggest you send your lens to Nikon for repair. It will comeback like new and you will not have to change your shooting style

As a sports photographer, I use my 300 mm f/2.8 the most when shooting field sports.

When I'm shooting basketball from the baseline, I use a 24-70 mm f/2.8 at the basket nearest me and on a different body the 300 mm for shooting cross court.

I shoot motocross (from within the track) using a 18-200 mm. With it I can shoot three turns, two straight aways and two jumps

When I shoot NHRA events, I use a 24-70 mm lens.

The only time I use a 105 mm lens is when shooting models or macro shots.

As you can see, if you follow your path shooting mainly sports, you will end up with a variety of lenses