In General the 756 series has few issues from a "normal" use aspect. Nearby lightning strikes and voltage surges do the most damage.
Occasionally I get in a 756 that won't power up. This is usually the Main unit 5v regulator or the main Dc/Dc converter on the sub-logic unit. This is rare though.

ICOM 756 LCD
The Original LCD for the 756, "Blue Lines", is still repairable, but it is expensive. The LCD is now a "factory-Japan" serviced part, so this repair takes a little bit of time. The Needs to go to ICOM, they pull the LCD, send it off to be repaired, and re-install when it gets back. The last cost I knew of was $340 plus shipping, but you should contact ICOM for the current charge. Any other repairs I am sure would be additional. At least it can still be repaired.

A company in the Netherlands has developed a replacement LCD for the 756. Right now about $300 shipped. This is less than what ICOM wants. Which is running about $450 right now. Here is there site Ham Tech Center