well of course it won't place - it's trying to be upside down! When I grab a driveway the part that is supposed to connect to the street faces the BACK of the lot, and it is in the middle part of the lot. It can't be dragged to the street, or turned the right direction.
This is a lot I made, on a terrain that does not show roads, except in lot view. So I removed the road "floor tiles", and replaced the sidewalk with other tiles. The yellow cone at the bottom of the pic mark the middle of the road. I've done this before and it didn't hurt anything. Portals still work (people go to work & school, mail boy shows up & leaves ok). And in other lots driveways can still be placed.

Are you using rotatable driveways and moveobjects on? That should be all you need to place them anywhere you want. http://modthesims.info/d/515924

Move-objects didn't help; I'll try the rotatable driveways.
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something's interfering with the rotation controls - works for other stuff, but NOT driveways. And can't move driveway to street. Can Sims use a care that's NOT on a driveway?

yes they can if they're able to jump into (there must be enough space for sim to reach a car door). You just won't see beginning of the animation.

You can't rotate driveways without the mod.

Before rotatable driveways, we used to remove one pavement piece from across the road and this would swing the driveway dependent on the sun. My guess is you inadvertently trigged that- once done you can't undo it unless you notice and hit the back arrow to get back before deleting that tile.

If that's what happened picking up the lot and setting it back down again should fix it. If not that, then putting it in the lot bin and replacing it definitely will reset it.

Probably, hadn't thought of trying that.

I have a lot uploaded here with a sidewise garage, it took me ages fiddling and figuring out how the sun position made it swing and I was so proud of it - Moo came out with the mod only a month later!

I got the mod and that didn't fix it. But it did work to just set the driveway where it was (at the back of the lot). GOOD INFO about the pavement across the road, and about moving the lot. But I just left it as is; you might have noticed the build it pretty strange; it's supposed to be really whacky aliens. So having them get in a car that disappears works for me. Thanks ALL!

I saw that but never downloaded it because I almost never make side garages... except for the last two houses I built and now this post. I think the universe is trying to tell me something.

I'm glad the unusual placement is working for your aliens, grammapat!