I started a new game and when it was time to pick up Lydia in Dragon's Reach --after becoming Thane of Whiterun-- she was not there. It is as though she were cut from the game. Moreover, I haven't installed new mods in the past two or three days that would cause her disappearance from the game?!?She was with me until the end in the previous game. I only started the new game this morning. I have even uninstalled the game and replaced the Data folder as well as the current save files: and, still she does not appear anywhere. Oh., how I long for the day when I can play this game glitch free!

try this:

open the console and type player.moveto a2c94

...and if that doesn't work, try a2c94.enable and then try the moveto command again. (I realize there's no reason she should be disabled, but just in case...)

After I became Thane Lydia walked to the house on her own. I happened to see and followed. Did you look there?