Re: Steam isn't working.
There should be a ClientRegistry.blob (capitalization is important in Linux), or at least mine has that in ~/.local/share/Steam/
During some update last summer Linux steam stopped working properly and the fix was to rm something. Now that I think about it appcache sounds very familiar. So that fix might have been: rm -r ~/.local/share/steam/appcache
But since I am not absolutely certain that would be a fix, you could instead try temporarily renaming that folder in ~/.local/share/Steam/ to something like appcache-backup and see if steam runs or updates itself and runs.
Note that Steam Cloud keeps track of what games you own, so even if you install steam from scratch on a different computer or OS, any of your games suitable for that OS should show up in your Library. The Cloud also keeps track of items and achievements, at least for most multi-player games, but might not for some single player games, especially those under development. For example when my Linux partition failed and I installed steam in Win7 my TF2 items/achievements were there. And likewise when I installed Steam in Win7 on new gaming laptop, and then in Ubuntu 13.10 once I figured out bumblebee (optirun).
i5 650 3.2 GHz, 8 GB, nvidia GTX 1060, 32" 1080p & assorted older computers