A dead laptop with no obvious cause means diagnostics equipment is necessary. Only a few laptop repair centres have such equipment. Those that don't have any just don't want to know when it's completely lifeless.
OK, pull all parts from the laptop (disk, memory, any mini-PCIe adapters liek the wireless card. See if you can get it to post (google beep codes). If you can get it to post then add back parts until it stops working and replace that part.
If the notebook will not post with all the parts removed then it's MB or something expensive. Buy the EXACT same laptop with a broken screen on ebay and see if you can move your screen to that laptop, or that laptop's MB/CPU to your laptop. Note some laptops come with two different lcd panels with different MB controllers. You need to match exactly.
For me with $350 laptops available new it's just not worth the hassle to fix.