New fixture won't turn on
Generally speaking, you must connect ceiling live cable (CL) to fixture live (FL) and ceiling neutral (CN) to fixture neutral (FN). As comments state, your fixture may not have a ground cable (strictly speaking), but some kind of screw, most probably with proper designation indented on it or with a proper sticker. If that's so, your ground cable from ceiling (CG) will match fixture attachment for ground (FG).
That said we have:
CL > FL
CN > FN
CG > FG  

Note 1.: There is a possibility that your fixture may not have proper attachment or cable for grounding. It may happen with old fixtures or these not exactly matching codes. Not preferred to fix. If you omit the grounding step, the fixture will probably work, but it's not recommended.
Note 2.: Screws on fixtures may have designations like N (for neutral) or L (for live). That may help you with doing proper matching and fixing.