It wouldn't be cheap, especially if you don't DIY itthe trench drains are expensive as crap. You'd probably have to rent a walk-behind saw to make a clean cut in your asphalt and then install the drains across the driveway to allow water to flow.

Here's another cheap option that I've actually done myself in a few problem areas of my side yard where I can't easily pipe a drain system to daylight - use post-hole diggers to dig a ~6" diameter hole down about 24", then put a section of perforated 4" pipe with a filter sock in the hole, surround it with drainage rock, and maybe throw some rock inside, too. Then you can put a cap on it on grade (can be something as simple as the one below) and it at least allows water to get below the surface and percolate into the soil more easily than just sitting on top of the ground. In a heavy rain, it's not going to prevent ponding, but it should help the ground dry out a little faster in between rains. You can even do a series of these holes it needed. It's definitely not a "fix", but I've found that it does help.
[Post edited by MP4VT2004 at 03/25/2022 5:29PM]