Apple TV 1st Gen not in iTunes devices or preferences

Question

Not sure how many other people have had this problem, but if you find that your 1st gen Apple TV disappears from iTunes devices and preferences this is what I had to  do to get it all back:
In brief I believe this is linked to the email @mac and @me alias's and my inability to keep everything in sync.  If this is obvious to you my apologies, but looking at the threads out there I think more than one person has this problem.
I had a 1st & 2nd gen Apple TV, an iMac with Lion, an iPhone 3GS and iPad 1st generation not talking to each other - they had all communicated perfectly well over the last few weeks and months (post and pre Lion upgrade). 
A few days ago (after the latest iTunes update 10.4.1 (10)) my 1st Gen Apple TV disappeared from the devices section of iTunes and so after much reading of communities to find an answer (no joy) I decided to remove it from the iTunes Apple TV sync menu in iTunes preferences.  I then couldn't get it back and it disappeared from the iTunes menu.  Heres how I fixed it:
When Apple changed the mobile me accounts from @mac.com to @me.com I started using both, e.g. [email protected] & [email protected]. 
My iTunes account on my iMac was set up to my @mac alias but I turned on home sharing with my @me email address. 
All my devices listed above were set up for home sharing (except ATV 1st gen) with my @me alias and worked fine until recently
In the last week I have regularly had issues with my 2st generation Apple TV password / email alias not being recognised by the iTunes store.
In addition my iPad, iPhone and iPod touch have also had issues with the remote app with both Apple TV's where they have 'disappeared' from within the remote app.
Today I lost everything on every device.
Here's how I fixed it:
Factory restore Apple TV 1st gen and set up with @mac.com email address details (not my @me email alias)
As above for Apple TV 2nd gen
Turn off computer, iPad, iPhone, BT Home Hub, Netgear Wireless router, unplug Apple TV 1st generation & Apple TV 2nd generation (mains and HDMI). 
Go to shop to buy gin and tonic ingredients
Turn on BT home Hub and when completely booted -
Turn on Netgear router and when completely booted (make G&T during this time) -
Turn on computer and launch iTunes
Plug in Apple TV 1st Generation and select general > computers and the 1st option with the infinity logo
Apple TV 1st gen appears in iTunes (phew, drink G&T))
Register Apple TV in iTunes, rename it (to whatever) and thank goodness everything back to normal albeit with long re-syncing (but that's why I bought a seperate wireless router from Netgear in the first place, so not so bad).
modifyed my home sharing account details in iTunes from my @me email to my @mac email alias
Turned on iPad and changed home sharing account from @me to @mac
Apple TV 1st Gen 'appears' when I select add shared library along with iTunes from my iMac on the iPad
turn on iPhone 3Gs and repeat the above (as per iPad) - again everything suddenly worked again
Plug in Apple TV 2nd Gen and changed home sharing, itunes account to my @mac account from my @me account (NB: I was able to see my iMac in the computers menu on the ATV 2nd gen using my @me email alias before changing it)
2nd Gen ATV appears for the first time in a few days back in the remote app.
All back to normal.
Now this may be blindingly obvious to you, but just in case it isn't, I thought I'd write it all down in the hope it helps someone.  It may not be the email alias, it may just be resetting everything, but I did try that first before fixing it using the steps above.
Best wishes.

Answer 1

I assumed that by using time machine to import everything onto the new iMac that the new machine was effectively the "old machine". Maybe not. It was set to sync to the old mac, so will try setting up  the Apple TV again on it's computers tab.
Still worried that I can't find the "find Apple TV's" option in iTunes prefs though.