Here are your parts
Replacement parts for LRE30451ST models | AppliancePartsPros.com

Here is a manual which may help.
LRE30451 LG Electric Range Repair Service Manual - ApplianceDigest.com
You have to join the site to download the manual but it is free and this is a very good site for manuals and other info for the appliance repair DIYer.

Can someone tell me if it is the motherboard or the actual burners?
If both elements went out at the same time I doubt it is the elements themselves. It would be too big of a coincidence.
Try unplugging the unit for a couple minutes to see if it will reset.
Check the wiring to the burners to see if they use a common power wire/line. Perhaps it is a bad connection or wire.
Try disconnecting the element user interface (keypad) and reconnecting it.
They do not give much info on the stove top keypad but it does show 2 cable sets coming off of it. Perhaps they control different element sets so it could be that board.

This is a complicated piece of equipment so unless you can find something fairly easily or have electronics experience it may be worth getting in a pro. I would try to make sure if you do get a pro that they have worked on this or a similar (as complicated) unit.