Given that the camera still can take good and focused images, I will assume that only the screen is broken. I will also assume that you are "moderately" familiar with electronics.
With that in mind, you are the only one capable of choosing the "best" option :
You want to keep it
If you feel confident enough to unscrew some parts, you might want to open the beast to see if all the internal cable are correctly connected. $0
If it doesn't improve the situation, you probably need to change the whole screen yourself. The back light + screen is about $55 on Ebay. You can look at this video for help, it's in German and for a slightly different model but should be enough for you to know if you want to try.
I don't guarantee that it will solve your problem. The best way to isolate the faulty component would be to disconnect your screen, plug a new one and check that it works, thus ensuring that it is indeed a LCD problem. You can maybe borrow a compatible screen from someone and check it out.
Get it repaired
A shop will probably fix it for something like $90 (80€ at my repair shop).
Get a used one
You really like it ? Find an used one, it should be about $140 (it was about $200 when it came out in early 2014).
Get a new one
You can also consider that you are done with the ELPH 340 HS. Now is a time for a change, you are free to pick any camera you want and can afford, new or used, from point and shot to DSLR. $10 to $999 999.
You may be able to get a few dollars by selling your broken camera for parts.