You shouldn’t be hurting 30 minutes after you’re done lifting weights or cardio. If you are, you’re not doing it right.
If you hurt and take an aspirin (or Tylenol or whatever) and that one dose doesn’t stop the pain, then you’re REALLY doing it wrong.
It may take a long while to build up to things. I recall I used to have really bad asthma. It was so bad, there were times, I would hesistate to cross Michigan Avenue (in Chicago) 'cause I didn’t think I had enough breath to make it all the way across.
My doctor said I should start cardio to help my blood pressure, (The upper number is in the high 120, the lower number is fine in the 60s). I was like, “I can’t walk without issues, how can I run.” She said to try. It took a LONG time, but in about 2 years I was able to run for 60 minutes straight keeping my pulse in the 140.
Oddly enough the blood pressure stayed the same but the asthma almost completely disappeared. Whereas I was using two or three inhalers a month, my current inhaler is almost two years old and I still haven’t used it all up.
So it may just take time. A long time, especially if you’re out of shape.
Also you could be very bored. Have music when you run. Or better yet, what I do is get books on tape. This is GREAT. I have “read” every book I was meaning to read, but didn’t have time to get around to by listening while running.
Also remember to vary your machines, don’t always do one. Try the bike, try the elliptical, try the stair climber (boy is that hard) and even swimming which is great, but make sure you actually swim and not just float around 
I really think if you’re otherwise healthy that it’s probably a combination of boredom mixed in with trying too much.
Perhaps you could split your routine. Do half on the elliptical, while listing to music, then get a book on tape from the library and listen to that while you bike.