Are there any new socket motherboards that are also compatible with Haswell E cpu?
The 5820k is only supported on X99 boards. Your two choices now are either try to track down an X99 board on the used market, or toss the 5820k and go for a new CPU as well, you could carry the RAM over to a new build as it is DDR4.
You're not going to find new ones at a reasonable price because support and production has ended.
You have to search the 2nd hand market.
Your only choice is the used market - ebay, craigslist etc. If you decide to replace your x99 board, I'd look for a 2nd gen 2011-3 board released for Broadwell-E (Haswell-E is supported). Be prepared to shell out about $200. Otherwise, sell your 5820k and decide on a a new platform.
no physical damage just dead no light or anythingDepends on what the issue is, and whether the repair shop's associates are competent enough...
A burnt capacitor, for example - gonna need a replacement as well as someone who can remove the old one and weld the new cap on.