Find the serial number in “Settings” -> 'System' -> ”About phone” -> ”Status”-> ” Serial number” Check the sticker label on the device or the package box. Or check the sticker label on warranty card.
And read the Make & Model Number off the Silk Screen Printing on the M'Board. As you have quite rightly already found out not all apps work for all M'Boards and Windows itself is very Dumb.
It can not in most cases define what Hardware it is running on so at the very least you would need some form of third party software.
Of course if you have a NB it's harder but any Desktop would take all of a few seconds to open the case and read the Makers Model Number off the M'Board.
Col
Here is a easy way to find,
Start Run, Type 'dxdiag'.
You can see system model
The chipset information can be known by using any diagnosis utility but it will not tell you about motherboard manufacturers name. But the chipset information is what we need to get the drivers etc. So you better not open the case and check the chipset information from a hardwared diagnostic utility.
Some manufacturers websites have decent information but, you must have the service tag #, exact model # and dig deep in the documents tab of the support and drivers page.
Look for a specification list. There you can find a lot of information about the chipset, # of memory slots, max memory support as well as type of modules.
Just download CPUz
http://www.cpuid.com/softwares/cpu-z.html