I want to achieve an effect similar to this example I've attached. I'd like to make the text start off clear and gradually blur from left to right.
In addition, I wanted to make the image seem as if the channel is about to be changed on the TV. Basically having the static "noise" from the tv being applied subtly as if the channel is being switched like old analog TVs used to do. I wanted to apply the static to the right side of the image where the blurring is happening. Is there any way to go about achieving this?
That looks like a radial blur: Filter > Blur > Radial Blur (choose "Zoom" as the method.)
For the static, think about whether you want there to be white static on the negative space, or just black static on the letters.
I'd go for just static on the letters, in which case I'd use a layer mask on the text layer. You can use noise to generate noise on the layer, and adjust the contrast up and down to get the effect you want.