I recently repeatedly uninstalled, fully cleaned my system of anything TS related after the most recent Windows Update because Teamspeak would not open. The process would actually start for a few seconds however the application did not launch or log anything in its logs at all before the process exits completely.
Initially after cleaning up TS and reinstalling a few times I rolled back the latest Windows update and tried again. - No luck
During this time I had also been working on maintenance for 2 systems in the office both of which have mapped drives to the device which uses TS. Because this devices requirements in a home office/work setting files outside of system and application are mounted to a networked storage device.
It is actually quite common that consumer oriented applications will error when common system user folders are not in their default system location
IE the developer has implemented no logic to understand a non default system path - hard coding /user/documents when the program should actually read the target location of documents or not offering on install preferred paths. On a tangent I have also seen prosumer to commercial grade software error on this when purpose built for environments where mappings are common.
While Teamspeak I have never seen use Documents Downloads Pictures Video (default user profile folders) I suspect that Teamspeak has some sort of startup requirement for the presence of these folders. While a feature may not be used and I have never used it I know that files can be shared on Teamspeak so perhaps those default to user folders and has not logic to read target data on those folders.
Teamspeak failed to launch and generated no error or log due to a mapped offline DOWNLOADS user folder.
This issue was resolved after maintenance of a remote share was down resulting in the computers User/Downloads folder being inaccessible. After share was onlined Teamspeak launched immediately.
Teamspeak in this case was installed in %appdata% and has no files or executable in a non standard directory.
This is a bit silly and a edge case but it is certainly interesting and if possible needs some improvement on error/notification of the process being killed preferably the application is not prevented from launching but presents a error but at least a log event.
Interestingly for the very long time I have had this setup (many years) Teamspeak does not appear to have issue running with mapped network drives (that are unrelated to the ability to launch the application IE executable lives locally so long as the drives are online).
Edit: I have been using TS5 this was initially a problem and resolved using TS5 however I did want to mention that during the course of my troubleshooting I did also consider the windows update clash with 5 specifically so I did replicate the failure to launch by installing TS3 as well.