People saying ride your bike to work, if he's spending that much money on gas in a week, it doesn't look like it's a reasonable distance to bike.
You can always combine it with public transport, to get a better mix.
Still, if it's not too hilly, you can do that in <2 hours. Maybe a bit slower in the morning, and a bit faster in the evening, if you can't shower at work, and need to be presentable.
Also, what kind of car do you drive, that takes 70 euros worth of fuel to do 450km? Any halfway decent Diesel hatch should be able to cut that cost in half.
See if you can get a more economic car for the long run. I put only 98 into my 1.6, and drive it like an idiot, and still only top out at 55 euro for 450km. (in France)
Ask your family for a loan to fix the car, if you really want it fixed.
Maybe you can put the repair off, and loan a scooter for the interim.