Which events are you entering? There's a limited number of events in GT4 that're considered "Championship Events" rather than "Single Race" events.
There are none in Beginner Hall.
In Professional Hall there's:
Tuning Car Grand Prix (5 Races)
World Classic Car Series (5 Races)
World Compact Car Race (5 Races)
Gran Turismo World Championship (10 Races)
In Extreme Hall there's:
Gran Turismo All Stars (10 Races)
Dream Car Championship (10 Races)
Polyphony Digital Cup (10 Races)
Formula GT World Championship (15 Races)
In Japanese Hall there's:
Japan Championship (5 Races)
All Japan GT Championship (10 Races)
Japanese Compact Cup (5 Races)
In American Hall there's:
All American Championship (5 Races)
In European Hall there's:
Pan Euro Championship (5 Races)
British GT Series (5 Races)
Deutsche Touring Car Meisterschaft (5 Races)
Tous France Championnat (5 Races)
Europe Classic Car League (5 Races)
Euro Hot Hatch League (5 Races)
1000 Miles! (4 Races)
In Manufacturers Events there's:
UK, Lotus Elise Trophy (5 Races)
UK, Lotus Lotus Classics (5 Races)
France, Alpine Renault Alpine Cup (5 Races)
France, Citröen 2HP-2CV Classics (5 Races)
France, Renault Clio Trophy (5 Races)
France, Renault Megane Cup (5 Races)
Germany, Audi Tourist Trophy (3 Races)
Germany, BMW Club 'M' (5 Races)
Germany, Volkswagen Beetle Cup (5 Races)
Germany, Volkswagen Lupo Cup (5 Races)
Japan, Mazda NR-A Roadster Cup (5 Races)
Japan, Mazda NR-A RX-8 Cup (5 Races)
Japan, Mitsubishi Mirage Cup (5 Races)
Japan, Subaru Stars of Pleiades (5 Races)
In each of these championship events you can click on the races individually or in the "championship" event (which is the first circle you come to with a "GT" logo in a shield flanked by chequered flags). If you've entered a championship rather than a single race, then you will see it will say "_____________ Championship: Race 1" etc. and you'll also get the icons at the bottom of the screen for "Practice" and "Abandon All Championship Events". If you're not getting these, you're not entering the championship properly, and thus won't get the Championship prize money & prizecar.
Also you can tell if you've entered a championship if you use the green icon to "exit race". If you're in a championship it'll ask if you want to return to the home screen (where you'll see flashing orange text in the top-right corner of the screen telling you which Championship you're competing in, and it gives you to opportunity to go into "Home" and save your progress, but it won't let you enter other events without giving you a warning.) If you've only entered a Single Race, you'll just exit, without warning back to the race list for the event you've entered.
(Edit: Tree'd by shorter and simpler answers while I was composing this essay!!!
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