Congrats on the fix! My daily watcher is a Sony 36" LCD that I got the same way--trash pick then replace a few bulged caps.
As far as tape goes, it all depends on exactly what kind of tape. 3M makes a line of double-sided tapes that are recommended as replacements for rivets or other mechanical fasteners. Some SERIOUSLY strong stuff:
http://solutions.3m.com/wps/portal/3...apes/VHB-Tape/