Keep in mind that if this dishwasher is old enough, replacing the whole thing could be better.
Yesss... this is the way! Ending is better than mending, as we all know... you wouldn't want to be seen as the kind of person who uses an obsolete dishwasher, would you? Think of what they'll say about you...You said you checked the supply lines for kinks, but did you check the inlet valve?
Shut water off to the dishwasher, pull the kickplate, and you should be able to find the inlet valve. If the dishwasher isn't filling properly, either that's clogged, bad, or isn't getting proper power.
Remove it, see if there's a inlet screen on it. If so, pull that out and clean it out.
You can also check to see if it's getting a clean 120VAC on the pins while running. Various wiring faults can lead to that valve not getting enough voltage/current to operate, and if you measure the drop across it while it should be open, you can tell if there's a wiring fault somewhere in the dishwasher that needs to be addressed (I believe the handle cutoff switch is often a problem).
If it's not clogged, and it's getting a full 120VAC, replace the fill valve. They can go bad and stop working properly. It'd be easy enough to hook a bit of spare tube to the end, pull it out from the dishwasher, and start a cycle to see if you get good flow.
Otherwise, keep troubleshooting. But your problems seem consistent with a bad or improperly operating fill valve.