Outside shade still doesn't compare to high school caves gyms.
Yes, equipment matters for low-light sports venues. Most digital cameras are so terrible at ISO 1600-3200 that you'd be better off shooting film. Either color Fuji 800 pushed to 1600 or 3200, or TMAX 3200 pulled to 1600 or used at rated 3200.
In all cases, you need f/2.8 lenses, no way around it.
A cheap option is a 50mm 1.8 for basketball, or an older pawn shop 100mm prime for volleyball.
For baseball, a 180mm prime is a low-cost option.
I can shoot 1600-3200, in some venues, on my D200, using my best lenses. But it's hit or miss. High schools are generally far too terrible for it, in terms if lighting, so it's more miss. The D300 isn't much different.
The Canon 5D most closely resembles Fuji 800 pushed to 3200.
I time most of my shots still to this day, just like I had to do when I was shooting a Canon AE-1 with film. So lots of frames per second isn't really something that is required. Indeed, it can just give you too many images to sift through. I do use it for some things but never a burst of more than 3-4 shots.
I would not shoot volleyball slower than 1/250th, due to body movements. With my D3s, of course, I can shoot far faster, which is nice (although not necessary).
I didn't start out shooting flagship models with top glass. For many years I had to make do, learning what could be used as a lower-cost alternative way. For sports (cheap indoor non-pro facilities), you have little to no wiggle room.