We have an old ford telstar, ayaw mag start ngayong maulan ano kaya yung problem?

Here are some details:

- carb engine, last month I cleaned the carb
- the timing and idling have been corrected a few weeks back
- the spark plugs were replaced around april of this year (however bec. the timing was advanced, the plugs may have fouled up or something)
- the fuel filter was replaced around 3+ years ago (i'm thinking this may need to be changed also)
- battery was replaced today, the old battery was 3+ years old and gave up
- last month we had to tow the car with our other car to get it started, it took quite a while though
- car is used only once to twice a week, travels about 100km a month only

Ano kaya problem nito? moist lang kaya yung plugs or car? we will try and push start it tomorow. If that wont work we probably have to get a mechanic to replace the fuel filter.