That's not the issue though. I've seen plenty of servers with 50% free RAM (16 GB total with 8GB free) who experience slowness. It's due to the RAM devoted to the SQL cache being full. It has to constantly cycle data in and out. When it's empty, there's mainly one operation and that's data entering the cache (one-way). Once it fills up, it has to flush out bits of information. So for something to go into the cache, something needs to go back to the disk (two-way). That's where the slowness happens.
Rebooting essentially flushes that cache. When you restart SQL server will only be using 50-100MB, as the week or weeks go on, this will get closer and closer to the 1GB limit. Once it gets there, that's when you feel the slowdown. You could have as much free memory on your system as you want, won't make a difference since it has to go back to the disk.