I put my Titanium armor and my Hellstone Sword and other good stuff into a chest on my server, and went to join the server from my new computer and pick up my equipment. But my character got stuck so I turned off my computer, turned it back on again, went into my world, and now my equipment is gone. What happened?
If you turned off the server without saving, then it won't have saved the contents of the chest... but the player character that put the items in the chest will have lost the items as well. In other words, your items are gone. I hope you had a backup of your .plr file, or else that you at least remember what you had.
If you need to replace your items, I would recommend using my favorite player editor, YellowAfterLife's "Terrasavr" found here. If that one doesn't let you save, try the flash version of it, which is linked on the right side of the other version. In my personal experience, Terrasavr can do just about anything to a player character. One time I even used it to make what I called a "creative mode" character (in the Minecraft sense of the phrase). It was basically a new character with a shroomite digging claw (this was before 1.3), vampire knives, 999 platinum coins, 500 HP etc. etc.
If you exit Terraria unsave , (Everything that isnt 'Save & Exit') items will disappear since the Server isnt able to synchronize fast enough.
You have to wait a certain time after picking up items or browsing through chests to quit Terraria unsave.
To gain your items back , simply start a singleplayer game and use the /give [item name] [playername] [quantity] command.