check engin light on on 2003 Toyota Corolla

my check engine light will not go off.i have disconnect the postive cable,to reset. it went off last year and then came back on. the problem occure is every day. i have two code p770. which is the soloneid switch sticking . i had aamco to replace it last year but it is still reading the same code. also the second code is p420. how do i pass my emission test

P0420 is low catalytic converter efficiency. It is an expensive code to fix. Usually it is a sign that the cat. convt. has got lazy but it is sometimes a O2 sensor/air fuel ratio sensor problem.
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you need to have it fixed. get a diag and repair on the trans code and a shop for the code for the cat. clearing the code does not fix it. you need to address it before it becomes a bigger problem.