Any of you "hip" to plumbing?

Here's my problem:

I am finishing our basement; the house is close to 30 years old and the basement is dry/stable as far as the walls/floor go. But there are two drain holes in the floor that occasionally "spit up" water, usually during very heavy rain/flooding (such as we have had recently). It's not much (small puddle maybe a foot diameter near each hole) but I don't want even that. As far as I know, these under-basement drains are not tied into anything except perhaps some exterior downspouts, which originally dumped into PVC pipes buried vertically in the ground. I suspect these originally carried the rainwater away from the house via underground PVC pipes that eventually dump outside somewhere.

I have disconnected all of these except two (which I just disconnected yesterday), chiefly because I'm concerned the pipes in the ground are clogged (the gutters/downspouts were not cleaned when we bought the house and have never had screens) and that the rainwater coming in from the downspouts is what's gurgling up through the drains in the basement.

Since I don't need the drains in the floor in the basement for anything, I am thinking about sealing them tight with RTV/lid of some kind. I don't want to make it permanently sealed (like a concrete plug) in case I ever need to access them for some reason - I just want them sealed "waterproof tight" so they don't upchuck water into the basement.

Any thoughts/advice?