I'd suggest first trying the "Upload and Install" method, i.e. go to Extensions, Install/Uninstall, use Browse to pick the installation ZIP file and then click on Upload and Install. I tried that on a number of Joomla! 1.5.26 sites (local and live) with different PHP versions, from 5.2.7 up to 5.3.10, and it works. One important note: if your host has upgraded to PHP 5.4.0, don't expect Joomla! 1.5 to work properly (or at all). Joomla! 1.5 was designed to run on PHP 4 and, as such, it is using some deprecated language constructs will behave erratically or throw fatal errors under PHP 5.4.x.
If this approach results in a blank page, Admin Tools' own updater is the next best choice. The Live Update will download the ZIP file (one page load), extract it to the temp directory (second page load) and then call com_installer to install from the temp directory (third page load).
In case you have a very restrictive and/or dead slow server, use the temp directory method.
At any rate, I would not recommend uninstalling and reinstalling, as this will cause all your settings to be lost. Instead, I'd recommend the manual uninstallation method described in our release announcement as it will only remove the files, not the settings. However, if all else fails, you can always try uninstalling and reinstalling, but you will have to reconfigure Admin Tools from scratch.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!