Please go through ALL of of the solutions below by trying one then testing to see if it helps with crashes when Picasa starts.
The Picasa version on your computer is outdated or corrupt. Install the latest and last version: How to get the final Picasa version
Quicktime player is outdated. See warnings about using QuickTime here: https://sites.google.com/site/picasaresources/Home/Picasa-FAQ/picasa/troubleshooting/i-can-t-watch-videos-in-picasa#TOC-Re-install-codecs
You may be missing a required video codec. A 'codec' is basically a program that compresses your video and allows for playback. You'll need different codecs depending on the type of video file you want to play. Visit http://www.filehippo.com/download_klite_codec_pack/ to download and install the proper file.
Windows Media Player is outdated. Go to the official Windows Media Player site to see how to install the latest version. https://support.microsoft.com/en-us/windows/get-windows-media-player-81718e0d-cfce-25b1-aee3-94596b658287
The Picasa database is corrupt and needs rebuilding. Follow these instructions: Rebuild Picasa Database
.mov and .3g2 files can cause problems. In Windows Explorer, move any .mov and .3g2 files to a folder that Picasa is not set to scan (Tools > Folder Manager).
Windows crashing is ALWAYS a Windows issue. Windows (or any operating system) is not supposed to crash. In fact, if Windows does crash, it's either a Windows bug, a hardware bug, or a bug in some "trusted" driver. Visit the website of your video card manufacturer to check for updated drivers for your card.