Model Ruud UGDA-12EA-GR 1983
The first problem was the fan would run non stop. I was told to check the t-stat & wire (ok) & then to remove the wire from the (G) termnal on the furnace. I did & the fan turned off, so I replaced the t-stat & now the burner & fan won't turn off.
Should I replace the Fan Limit Control next?

It sounds like it's wired wrong. You will get nowhere fast replacing parts without knowing if they are good or not. Why don't you get a meter and then you can do it right. I teach children to use a meter and they do well on young as eight years old, so I know it's not hard to learn. Remember: W goes to heat, G to fan relay, Y to the contactor for AC, and R supplies power to other side of these switches, and C is common on some t-stats. Common is the other side of all the previous relays. You can test the fan switch and check it. It has an on/auto switch on it to make the fan run off the t-stat built in or on all the time (manual). It could be switched on, too. If you do get one get the right length of sensor. Look at: https://dl.dropbox.com/u/8010163/How%20to%20use%20Test%20Equipment%20Service%20Manu al.pdf
https://dl.dropbox.com/u/8010163/AC%20Wiring%20Diagrams.zip