Garen is definitely still a great Champ. Just keep practicing and trying different builds. Just make sure to buy at least 2 good items for HP. Don't be afraid to have some bad games.
You say you're having trouble closing the gap/catching to kill them. Use spells like Exhaust or Ghost, or both. Also, don't forget you can buy those extra speedy boots of swiftness. Other boots may seem more useful but what good are they if you can't catch anyone to use their buff. I don't see too many Garen's using Frozen Mallet but I'd say it's never a wrong purchase for melee champs. One hit from you and they have to commit to a fight because they won't get away until someone dies. It's you or them!! F. Mallet keeps opponents from kiting you. Which means they do a little dance to and fro and back and forth (as if they were a Kite attached to a string, attached to Garen), just 3 steps away from you and poke at you with some range. Don't Chase them too far, and counter the kite with a bit of your own by moving back and staying moving.
Good luck, Brickey.
P.S. Garen isn't supposed to be (doesn't mean he can't be) a super great 1v1 champ. And don't be afraid to use his Ult a step too early. It doesn't have to be the killing blow. With a bit of a Tank blend build Armor and HP and let a teammate help do some of the initial ranged damage so the fight starts with the enemy at 70% health.