Semen contains sperm which combine with ova (provided by the woman) in a process called "conception" to create a new organism which travels down to the uterus and attaches. At that point, you're considered pregnant.
Thing is, if a sperm cell (or ova) is dead, it can't conceive. If there is no ova present to combine with, there is no conception. If the conceived cells do not embed somewhere (one hopes, the uterus) and start to grow, you're not pregnant.
OK, so in this case, how long can sperm stay alive when exposed to air such as if they are hanging out in a laundry basket? As soon as the semen dries, the sperm dies. Yes, sperm can survive in warm water for a few minutes (perhaps 5), but ultimately, if a given cell isn't surrounded by the rest of the components of semen, it will die pretty quickly - dousing in water will dilute the semen making it unable to support the sperm cell.
TL;DR although I won't say it is impossible, the likelihood of you getting pregnant by touching dry soiled laundry is, essentially, zero. The probability of getting pregnant if you touch it while it is still moist (hasn't dried out yet) and you then place your hands in or near your vagina is still ... really really small.
No, you're not pregnant. Or at least you didn't get pregnant THIS way.