BLOCKED_TIME generally means a period when the thread wasn't doing anything at all. This could be periods of I/O, where network or other types of latency are involved or time spent waiting on locks such as in situations with semaphores. In short, this doesn't necessarily tell you anything, as there's perfectly standard and reasonable reasons for the thread to be idled. However, a goodish amount of time spent blocked can be an indication of an underlying problem. Perhaps you have too much network latency. Perhaps you're trying to do too much file system work on a slow drive. In short, it may or may not indicate a problem, and even if it does indicate a problem, it doesn't really tell you what the problem is.
In general, if you're experiencing thread starvation, the first thing you should look at is thread pool utilization. Are you using async everywhere you can? Are you doing things that are big no-nos in web apps such as using Task.Run, Task.StartNew or worse, Thread.Start? All those created threads are coming out of the same thread pool, and thus proportionally reducing your server throughput.
There's an all too common pattern of attempting to schedule long-running jobs by shuffling them to new threads. That's death to a web application. All threads in the pool are there to service requests, not long-running jobs, and as such, requests should be handled quickly and efficiently so that the thread can be returned to the pool in short order to field other requests. If you need to background work, you need to truly background it, by offloading to another process or even a different machine entirely.
Short of all that, maybe you're just getting more load than the server can handle in general. That's always a possibility. Perhaps you need to vertically scale your system resources (and the thread pool with it). Perhaps you need to horizontally scale by replicating this server with a load balancer in front. Given that you're running multiple different things on the same server, an easy way to horizontally scale is to simply divvy out these things to their own machines. That alone would probably help tremendously. However, scaling, either vertically or horizontally, should be your last resort. Make sure you're using resources efficiently first, before throwing more resources at your inefficient things.
