[Joe Horner]

Do both battery prongs press against the battery, or does one stick up & contact the case back? I ask because the alarm function isn't working on my 7T32, but it's also currently in low-battery mode (which I know may explain it as well).

A little late to the party on this but:

The alarm contact is the small, gold plated, one marked in the photo below. From memory, it's a "loose" contact and may well have dropped out either when you opened the case or on a previous battery change.

One other point from the original post, the correct battery for this calibre should be an SR927W ("high drain") not SW(low drain). The 3xx number is 399, not 395. Using a low drain won't be a problem for normal use but will lead to a big drop in battery life if the alarm and / or chrono functions are used regularly