By the way after 3 days of baby induced minor sleep deprived brain damage, I know whats wrong with your dryer.
Theres a blower fan that draws air through the dryer and exhausts it out the vent pipe. If you take your vent pipe off, you'll probably find that there is no air (or significant air) coming out of it.
Unfortunately even if you found the repairman with the part, it'd probably cost you $100 at least. I'd go with the new dryer.
On the other hand, if you can find the part, its probably a piece of cake to put it in. Couple of screw clamps holding it to the ducting, couple of screws holding it in place, two wire electrical plug, you're done. Unplug it and tip it on its back, see what you see. Dryers (and washers for that matter) arent that complicated.
Al - ventless dryers or running your dryer vent through one of the many available doohickeys that let you 'recapture the heat' into the house are a very, very, very, very bad idea. I know of someone who did that regularly for about 20 years and ended up with a delightful case of mold and mildew, along with some nice hidden rot.
If you're in the winter time, using forced hot air heat, and regularly using a big humidifier to keep the air moist, and you have a way to circulate air throughout the house, you might get away with this for a few loads a week with the dryer providing humidity in lieu of the humidifier.
Keep a humidistat and keep your humidity level between 40-50%. When you stay at 50%+ sustained, you start getting mold and mildew.
I'm thinking the Eureka area doesnt have a problem with low humidity...?