Help GS4 keeps vibrating, screen acting as if it's not on, is there a fix?

[Inmento]

Last night and this morning my GS4 (5.0.1 if that's needed) was working just fine. It had died as soon as I got home from work this morning but I plugged it in and slept for the 4 hours before school. When I got up I tried to turn it on and I got the vibration and led flash as if it turned on but no samsung logo or anything.

I'm unsure if the screen is broken, as the back button and the settings button still light up as if I awoke my phone from it's slumber.

I've tried doing safe-mode and recovery mode, but again without seeing the Samsung logo, it's difficult and I most likely failed.

The phone is also on, I think, as I'm getting notified and it's vibrating but I cannot see the screen. It's as if the screen won't wake up when the rest of the phone does.

Should I just go for my eligible free upgrade with my carrier, or try to fix my phone?

 

[NickoPrime]

In your case I would simply contact either the carrier or Samsung, I would actually go for Samsung first because your carrier will try to contact the device manufacturer which is Samsung so you would be wasting your time if you call your carrier first lol.
You could try to let your phone fully discharge then fully charge it to see if it fixes it but I think that either your display died or your GPU died. In both cases, there is no fix, there is replacement but those parts wil cost you almost the same as a fully working phone so maybe it's not worth it.
I hope you did a backup of your data because it will be hard to get data from your device unless you saved your stuff on your sd card.

 

[Hadron]

You can use a MHL cable to mirror the display to a TV (check compatibility - Samsung use 11 pin cables, everyone else uses 5 pin). If it is just the display that has failed that will help you to get other data backed up.

Won't help if the gpu has failed, but that is less likely IMO.