vibration, shimmy, shake, square wheel?


First of all hello to everyone, I haven't been by here in a LONG time. Well I have been hit with the dreaded mystery shake wobble vibration bumpy ride issue. I just relocated from PR to Texas and before my bike was shipped and stored it rode fine except for a recently 2nd gear issue, but I know exactly what it takes to fix that and it never affected how the bike rides. Just to make sure I mention every detail possible, when the bike arrived the front tire was completely flat and could have been that way since I dropped it off for shipping. After airing the tire I rode it and immediately felt a shake of sort (left to right in the bars) and an even more noticeable bumpy feeling, as if the tire was not completely round. I have been out of town for a week but will return home to start working on it tommorrow. I did take it to a local bike shop just to check for propr tire balancing, the added the correct amount of Dynabeads.... I know I know, some people swear by them others think they are snake oil. Anyway there was absolutely no change. I also lifted each end of the bike and checked for true spinning of both wheels and didn't see any irregularities. No left to right wobble or up and down. They both spun freely and straight, also the issue stays constant whether accelerating or braking so I really doubt its a warped disc........ So my next step will be the most common issues, check and adjust my steering head nuts, and replace if necessary, wheel bearings, and cush drive bushings. ... any suggestions that might save me some time and/or money?
Yeah once I tighten the steering head, I'm thinking I will probably replace that front tire before buying anything else.
Rebalancing the tire would be a good first place to start. Wheel weights are cheap and balancing is easy. I think I got my harbor freight balance stand for around $35 w/ 20% off coupon. Or you can do the jack stand method.

But, in all reality if it was on the frt tire flat for a while, replacing it would be a great idea....

Check for the bent rim. Even if the tire is balanced, the bent rim can do that, and it doesn't take much. Get the flashlight, and carefully go around the rim.

Another possibility, make sure that both triple trees' bolts are tight. If one of them is loose, you would get the feeling you are describing.

Out of balance tires would shake only around certain speeds - when the respective wheel rpm creates a mechanical resonance.
Remember.......a lot of these tires have steel belts in them and if the whole weight of the bike was on a flat tire, it could have permanently deformed them. The easiest thing to do to start with is to just replace the front tire before you start taking everything apart and start measuring everything. You can rarely see internal belt damage on a tire by just looking at it.
Thanks for all the replies, I just got done disassembling the upper triple in order to check the stem bolts and low and behold it was about a half a turn too loose....I have the front wheel off too so before I put everything back together im gonna get it balanced again but gonna go with the conventional way this time. If after all that is done I will take it for a ride and see how she feels. If I still have the issue, my next move will be a front tire.