Check your disk stats, or memory. Most of the time when I've had high load averages, it's been because the disk system is swamped and there's a whole bunch of processes waiting on io.
For example, in the classic apache dos failure state, you wind up with enough apache processes that some of them are forced out of memory, and then you start swapping and fall over. What you'll see then is a really high load average and long page load times. Looking at something like vmstat 1 or top, or iotop you can see if it looks like memory, disk, or something else.
From your description, you probably have enough cpu resources to saturate something else. Maybe the DB server, maybe your memory. When that happens, your processes stack up and your load average rises. It looks like you don't have neough CPU, but that's probably not it.
For example, in the classic apache dos failure state, you wind up with enough apache processes that some of them are forced out of memory, and then you start swapping and fall over. What you'll see then is a really high load average and long page load times. Looking at something like vmstat 1 or top, or iotop you can see if it looks like memory, disk, or something else.
From your description, you probably have enough cpu resources to saturate something else. Maybe the DB server, maybe your memory. When that happens, your processes stack up and your load average rises. It looks like you don't have neough CPU, but that's probably not it.