How do I increase the size of inbox.

Talk to your email provider.

When was the last time you Compacted your Inbox to actually delete all the messages you marked for deletion?

The problem is that Thunderbird has limited my computer's storage space to 100mg. My email provider has no control over thunderbird. I compacted my inbox after deleting everything I could.

What makes you think Thunderbird has set a limit. This article says older version had a 4 gig limit but that is gone now.http://kb.mozillazine.org/Limits_-_Thunderbird