So I was adjusting my front mech, however the adjusting screws didn't seem to do anything. Later I removed the cables and now my front mech just clamps down towards the frame as far as it can. Is it broken?

Okay. Well, now you'll start from the beginning. Is the chain on the bicycle? If not, remove and thoroughly clean the front derailleur, then lubricate all of the pivot points. While you're handling it, notice how the two adjustment screws are labeled "H" and "L", for setting high and low limits. These screws make contact with a cam that defines the motion of the derailleur cage from its base. One on each extreme of the cam's movement.

Re-mount the derailleur, paying attention to align the main axis of the cage parallel to the chainrings. Height should be so that the cage (when swung outward) clears the large chainring by ~3 mm or so.

High is 'normally' on the large chainring, and limits the outer most motion of the derailleur cage while under cable tension from your front shifter. Low is 'normally' on the small chainring, and limits the inward movement of the cage, which you've described as "towards the frame" once you undid the cable.

You begin with the Low screw. Chain back in place, and on the inner chainring and rear innermost (lowest) cog. Begin to tighten the L screw and watch the cage move outward, until the inner edge of the cage (that contains the chain) just makes contact with the inner edge of the chain. Back it off until there's 0.5mm or so between the cage and the chain.

Shift down to the smallest (high) cog on the rear.

Now attach the shift cable. Make certain that it moves freely through its cable and guides, and that your shifter is in the "lowest" or most slack position. Pull the cable somewhat taught, paying particular attention to the binding bolt area. If there's a small metal tab just before the bolt, then make sure that the cable passes OVER that tab before clamping it.

Shift the front onto the front chainring. Note the position of the cage's outer edge and the chain. Cage too far? Then tighten the "H" screw until it limits the movement of the cage to within 0.5mm or so of the chain.

Unable to shift upward to the large chainring? The derailleur cam may be blocked by the "H" screw being too tight. Back the "H" screw off and watch the movement of the cage/cam as you attempt to shift.

There will also be a technical note on your particular derailleur, if you get the model # from the edge of the cage. Search technical documents and that model number. There will be diagrams.

Good luck. PG

Do the adjuster screws still do nothing without the cable installed?

I ABSOLUTELY don't recommend "jacking" the chain ring over with the limit screw.
The DER metal tends to be "soft" and doing so will result in undue wear on the threads.
You can hold the FDER over with your thumb and turn the screw some. Repeat as necessary.

I really agree with you, Bill. I winced a bit when I wrote that, but I was concerned that the OP would be overwhelmed by having to move the cage manually with a slack cable and simultaneously tighten the high screw until it kissed the cam when the derailleur was held min the correct high position. Easily done with experience, tougher to convey to someone who doesn't understand how the FD is designed.

Thanks for calling me on it. Phil