Like the title says. Bike hasn't been shifting very well lately. So figured it was time for a bath and to clean&lube the chain. Rear shifts just fine, but front doesn't shift at all. When I feel the cables underneath the downtube while shifting, I can feel the rear cable contract&lossen with every shift. But the front cable doesn't move at all.

So is this likely a broken cable, shifter, or something else?

Front shifter is a sora triple, but the newer one without thumb buttons.

Front shifting has never been great, for what it's worth-only ever been able to get two chainrings working at a time reliably.

My guess, and this really is a guess, is that your front shift cable is too loose or has slipped in the front derailleur's pinch bolt. Shift the front shifter into the granny (lowest gear) position several times to assure it's at the slackest. Check and see if the cable is very loose and has a lot of slack. If that's the case, loosen the pinch bolt, pull out all of the slack and tighten the pinch bolt firmly. If you are using a teflon coated cable, be sure to scrape off all of the coating where the pinch bolt grabs it.

How old is the bike? Shifters need to be flushed every now and then.

Detach the cable from the der's anchor bolt. Hold inner cable as close to the shifter as you can, maybe slide the casing off to get right up to the shifter cable port. While slightly tugging inner cable work the shifter through it's range. What happens? Does the cable move with each shifter position or not? If you start this hold the cable and shift close to the der then move the holding point up along the cable's route sometimes you'll find that the cable is snagging along the route at a specific point. Key to figuring these things out is to separate the various functions (der movement, cable movement and shifter function). Andy

What do you mean 'shifters need to be flushed'. Flushed with what?

usually flushed out with copious amounts of wd40 or the like then relubed with a light lube of choice, but I would follow Andrews advice first to ascertain whether its a shifter issue or a cable inner/outer friction issue and while you have the cable loosened swing on the FD to see if its pivoting and not seized

Does this mean spraying the bike with a garden hose? If so, you likely have rust inside every enclosed space, including shifters and cable housings. As others have said, you can restore operation by flushing with WD-40, but you should follow it with light machine oil. Tilt the bike so that cable ends point upward, and drip oil into the end of the housing. Hope that it eventually runs through the housing. Even badly rusted cables can be made operable this way. However, it's far better to keep water and detergent cleaners away from internal parts and chains.

Might try one of these to lubricate your cables.

https://ecx.images-amazon.com/images/I/41Gq54rgkYL.jpg

un hooked the cable/ housing set and tried it as a separate Item?

No, a sponge and warm water with hand soap.