These computers tend to be bricked if the battery goes completely dead or is removed from the computer for anything but a very short interval to stick a new battery in.
After lots of looking around the web, I came across a discussion about a voltage issue regarding "waking these computers up"...if I recall correctly (it has been awhile since I read the discussion), one needs to use a larger capacity battery along with some wires to "jump start" the computer...the level of effort was on the order of a complete pain in the arse but for those nostalgic for these older computers it might be worth the effort.
You do realize that the last post in this discussion thread prior to yours was 9-years ago? And the Suunto computer in question is quite a bit older than that? The Suunto Companion computer, was a decent computer in its day...and if it worked today would be a functional dive computer. But the reality is that the technology and functionality has improved, become more reliable since the Companion and the like hit the market.
There are lots of reasons to be sour towards Suunto for their dive computes...the inability to get their really old (and to some of us, obosolete) computers working after the battery has been removed for an unspecified length of time causing it to be a paperweight is just not one of them.
-Z
Edit:
Here is a link to a discussion thread where the "jump start" procedure is described...good luck:
Hi I have tried to change the battery on a Suunto Companion, but the damn thing just say "LOG", and its impossible to enter the menu. I have tried to shortcircuit it, connect all 3 contacts at the same time and drain it totally for remaining power, leave it without power for extended time...
scubaboard.com