Finally got it working, I think...
Sorry, I wasn't able to post back when I wanted to, because I had to brush up on knowledge a bit and even after that, my reception was spotty.
Here's the progress:
After I had gotten the info about my dish pointing at the wrong satellite, I tried realigning it with just the dish and receiver and someone helping downstairs. I had no success with that and assumed that I didn't get the right feedback from the Dish 501. I looked around on the web and found a very helpful article from an RV guy that had run into problems aiming the dish properly with just the receiver. Here's the url:
Anyway, it appears that the 501 won't even show a signal if the Check Switch routine had failed before and has no memory of what satellite(s) the switch is seeing. That means you have to aim the dish blindly first, then run a Check Switch, have it find the two satellites and peak the reception from there. I couldn't seem to get that to work and instead got a satellite meter at sadoun.com (http://sadoun.com/Sat/Products/Accessories/Meters/SF-95_DSS_Satellite_Signal_meter.htm
Armed with that (and an angle meter I got there as well), aiming the dish was pretty much a snap. Check Switch found both satellites and I got signals over 100 on almost all transponders.
You would think that my worries were over, but not quite. The signal kept disappearing after watching for a while (an hour, sometimes less, sometimes more).
New Dual LNB (probably didn't need that):
Reading around here a bit, I seemed to be left with the choice of a new dual LNB, or new cabling (or new receiver, but wasn't ready for that assumption). So I purchased a slightly used DishPro Twin LNB (with dish, because I didn't know that the switch is actually built into the LNB). But even after mounting that and aiming with my satellite meter, the problem was still the same (losing signal after a while on all transponders). BTW, the new LNB is not one of those CCS90... or something ones that have heat problems, I checked.
Slightly frustrated, I moved on to tackle the cabling issue. At this point I wasn't so sure anymore that it wasn't the receiver's fault, but cabling was a cheaper option, so I went with it. After some reading I realized that the initiall used F connectors weren't really recommended for outdoor use. They were the crimping kind, not compression sealed ones. My cheapest option was a 100' high grade RG6 cable with compression seal connectors. Got that for around $32 on ebay (seller jvlsks sells these all the time if you're interested). Didn't want to get bulk cable, T&B connectors and a compression tool. Would've been more expensive, I believe. The cable came today and I was not so sure anymore that it would work. Maybe it was my receiver all this time!?...
Anyway, installed the new cable without problems and ran a Check Switch. Both satellites were found, so far so good. When I went to look at the transponder signals though, only a few transponders had signals over 100, the rest were simply dead. Many important transponders were missing, or not coming in. Consequently, many channels wouldn't work. As a last resort I did a front panel reset and voila, when the receiver came back, everything was in order. I've been writing this post with the receiver on and so far so good, no dropouts or important dead transponders. I'm hoping it'll stay this way as I was almost ready for cable... (not that that works without problems all the time). But I just like the idea of receiving TV from space.
As a side note, it seems to make a big difference what 501 page you're on when you do a front panel reset. The reset seems to be most effective when you're doing it on the Menu>6>1>1 page (the satellite signal strength page). After fiddling around in times of signal loss, it seemed to get reception back when I was on 119, transponder 1. Doing the reset simply while viewing a channel did no good at all then. Your mileage may vary.
Thanks again to everyone for the great advice. This board is a tremendous resource. Didn't call DishNetwork once. Couldn't have done it without you guys.
crossing fingers for stable signal from herein...