Currently I'm using 3.5-185.
Default hotkey for saving states in dolphin-emu is Shift+F(1-8).
But when I'm pressed this keys dolphin says that state not found. It means that dolphin tried to load savestate instead to save it (Fn buttons work but Shift is not).
In Hotkey settings Shift and any other buttons works but not ingame.
Can you save and load save states via the toolbar menu? If not, it's probably not an issue specifically with the hotkeys.
I had nearly the same problem myself recently. 3.5 couldn't make save states (note, up until then I had never used save states at all in Dolphin) but it kept complaining that it couldn't find it when pressing Shift+F1, etc. 3.5-105 did create save states (dunno about loading them, just use them as insurance against memcard corruption).
Maybe try deleting all save states in your ~/.dolphin-emu folder or see if another revision will properly make save states. Fwiw, when compiling new builds, I don't make install them, I just copy the binary to a folder and run it (3.5 is installed though). Not sure if this has any effect at all.
Saving from toolbar option works.
Only Shift+Fn doesnt work.
When I'm changed Shift to CTRL or ALT in hotkeys menu it start to save normally (except 4th slot with alt button, dolphin crashes after saving).
The problem is in Shift button.