As you have been advised, it's possibly a trial and error issue you have here.
For many years I lived in Santa Barbara, CA, and our FM came from 100 miles away in Los Angeles. The best thing you could do was to put a 10 element FM ONLY antenna as high as possible and use good quality lead-in (open wire 300 ohm was best at that time) and orient the antenna as best you could for optimum reception.
Some stations would be solid for hours at a time, others would be sometimes very good and other times very noisy or not there at all. Depends on the weather and the conditons and time of day. The move to stereo on FM made things even worse as to fully quiet the FM signal requires a stronger signal when the broadcast is multiplex. You can help with that by using a tuner or receiver that will allow you to force mono reception.
Yes, horizontal antennas are best but many FM stations these days use transmitting antennas that include appreciable vertically polarization for the listeners in their car with vertical antennas.
It is likely, unless you have a very good tuner or receiver, that your car receiver is better and more sensistive than what you have at home. Thus perhaps the better reception from the car.
I thought that Radio Shack still had 4, 6 or 10 element FM only antennas but don't find any at radioshack.com. I'd suggest the cheapest way to try this all out is to find somebody with a decent fringe or near fringe TV antenna, perhaps still on a pole on their roof, long ago abandoned for cable or satellite TV. Some but NOT ALL TV antennas include appreciable gain on the FM band. Some brands had a design that purposely decreased gain in the FM band to provide less interference with Channel 6 so it's a crap shoot.
Put the "free if you take it down and haul it away" antenna on your own roof if at all possible as high as you figure you can safely. We always used to go at least 40 feet but 10 feet could work.
Use low loss coaxial cable with decent connectors on it. Make it as short a run as possible to keep the losses down. IF you discover after carefully rotating the antenna and locking it in the direction of greatest signal (could possibly not be in the exact direction of the desired station depending on reflections from tall buildings or mountains) that you get a signal that is near usable, then you might want to try an FM preamplifier either right at the antenna or in the feed line.
Having said all this have you checked to see if that station is available as part of the cable TV system? In the wilds of Nevada I would think that the cable provider would offer FM from LA and other nearby areas that could be received from their antenna farm. Perhaps for extra $$$. And have you checked to see if that station or an equivalent one broadcasting the same type music is available over the Internet?