My Sony 35" Trinitron TV (KV-35s40) was ON when lightning struck close by.
I immediately lost picture and just had snow on the screen. I confirmed
cable/satellite was ok by plugging the cable into a small tv for testing
purposes.

I can watch Satellite if I use the Svideo cable and the RCA plugs for audio.
I cannot get any picture to come in when I try to use the coax cable into
the tuner on the back of the TV.

Is it safe to say the tuner is bad and I can just replace it? It seems like
an easy enough job to remove it and solder a new one. Is there any other
type of "test" I can do to confirm the problem is just with the tuner? Or
did I already do enough by bypassing it and using the RCA plugs?

Any recommendations on a vendor for this type of part? I know I can just
Google the part number. I did find it easily.