Sony Xperia E4 - Responsive grey screen

Upon power-up the screen shows a flickering Sony logo, where the image jitters up and down - I proceed to try and type in my SIM passcode, but when the numpad comes up, the phone quickly fades to a grey screen with vertical, white-ish stripes.

The phone has been in the drizzling rain outside, and has endured the temperatures down to -30C and I couldn't find the LDI information anywhere to check the sticker for water damage. The top bar on the phone is still visible, although also jittery and flickering.

Further: It does work sometimes, there are white dots on the background here and there, and the screen looks dimmed. Then it fades again to the same grey screen after a while of use. Do I need a new screen or is there another problem?

- LeviK