It was on its way. Most people just shrugged and used the default browser (IE) and there wasn't much mindset that browsers were meant to be power tools - IE didn't even have tabs, it was just a window that held a webpage with a couple of back buttons. And IE felt
clean after AOL, which was many people's first browsing experience.
Among those who did switch, most switched to Firefox (and a small few switched to Opera). By the time Chrome was released, Firefox's market share was 20-25%, entirely through grassroots evangelism. It felt like a steady race that we were winning. Then Chrome came along with its minimalist interface, hyper-optimised JS engine, extreme attention to latency, and aggressive marketing from the front page of the internet (which was also growing more JS-heavy by the day), which contributed to Chrome not just feeling faster, but amazingly futuristic. Whereas Firefox was "you really shouldn't be using that crufty old IE, try this new hotness - it has tabs!", Chrome was more "OMG you have to try this, it makes your internet twice as fast". It didn't help that Chrome's strength was Firefox's weakness - for all its merits, its XUL-based interface sometimes made it feel a mite sluggish.