Attack on my mac (pls ignore first post)

(Norton staff, please delete my 1st post since it came out in a block and hard to read - thanks)

 

Hello,

Not sure whether this is the right place to post the following because the problem I have on my computer seems beyond NIS to prevent but a computer technician suggested the Norton forums so...

The problem is that my computer (OSX 10.5) has been hijacked. This problem has been ongoing for a couple of years now but has recently become more severe. What happens is that someone seems to remotely take over my mac while I'm using it although usually not so badly that I am forced off line.

It doesn't seem to be a virus because even if I do a clean install -- and I've done plenty, from 10.4~10.6 -- strange anomalies occur such as:

1) cursor flickers on and off as I move it across the screen using the mouse. It disappears when I stop moving.
2) if I run the cursor along the menu bar the drop down menu(s) will be highlighted further down and/or the highlighted part will sometimes run or even flicker quickly up and down the menu by itself.
3) Sometimes, for example, a little snitch window will appear (as it should) and it will 'rattle' from side to side while the speakers emit a sound as though someone is holding their finger down on the mouse. (I 'fixed' that by putting earphones in the jack)
4) Once or twice while online using firefox simple text suddenly started up (with the same 'machine gun' like sound from the speakers) and forced itself to become the active app. (over FFox). When I quit SText it simply restarted by itself (about 4 or 5 times).
5) Phishing(?) attack when logging in to my mail account online. After entering my password and hitting return a google page started up with my password clearly displayed in the search box. Happened a couple of times. Once I was unable to log in because one key would not type in. I do not have a gmail account.
6) That's probably been the main stuff that's been happening in recent weeks although other stuff has happened in the past.

I recently bought a new computer (both old and new are macbook pros but different models) but the problems continued. The above anomalies and more occur whether I am offline or online, makes no difference. I do not use my computer at an office etc so I don't think anyone has put a virus on it using a USB stick etc.

What I've done:
1) removed the airport card and bluetooth cards in the earlier macbook pro and disconnected the cable for airport/bluetooth in the back of the new mac. Airport doesn't show up in the system preferences of either machine.
2) took one of the macs to an apple store to get someone to look at it. It worked ok so the guy couldn't do much or offer any advice, even though I showed him videos I'd taken of the desktop while it was playing up.
3) Completely erased the HD and installed a new system as mentioned. Even before adding any 3rd party software (Nortons NIS, LittleSnitch, Net Monitor and Firefox) odd things occasionally happen. For example when setting the time it will disappear or change to 1969, as it did once. Or old settings I'd previously used will show up even though it's a brand new install. (Offline)
4) I've even tried installing Linux (unbuntu) at different times with no 3rd party software. Same problems but worse when trying to install. I did this offline.
5) Keep Norton anti-virus and so on updated. When I do a full virus check of my HD it comes up clean.

I am not a whizz with computers but was hoping I might get some guidance about what to could possibly do. It seems to be a remote attack, possibly using a cell phone tower(?), but I don't know how it's being done since airport and bluetooth have been removed. The person is able to commandeer my machine at will even though I've tried installing and using my computer in different locations, but always with the same results.

Thanks

Note; even as I've been writing this the cursor (but not the flashing vertical bar in the text box) has been occasionally acting funny as usual.