Keep or sell, but don't chuck them.
Records are always great – with the notable exception of when you are moving house. I always curse my vinyl collection whenever that happens.
EDIT – Just noticed that you don't have anything to play them on. If you're not planning on buying a new record player, then you may aswell sell or donate them to charity.
Melted vinyl records
As a toddler, I carefully placed a dozen or so of my dads 7 inch singles along the top of the fire guard and watched them melt. I am honestly surprised that I am still here to tell the tale.