After uploading 3 plugin updates, can't access my website or wordpress admin

One possibility is that you are running out of memory. I had a client who went plugin crazy (105 plugins installed w/ 32 active). He added one more and poof! everything disappeared. I looked at the error logs and he was running up against his memory max. Although you may be able to adjust this yourself, it is more commonly set by your hosting company and you can’t change it.

Try moving one (or more) of your plugins out of the wp-content/plugins directory and then try to reload your admin page.