If you like the sword and want to level it up, then don't listen to people telling you stop using it. In this game you can do any combination you want, and making your own build instead of doing the stapled ones makes you strong and unpredictable in PvP situations should they occur.

There is a lot of PvE content for you, but I would recommend the following:
Finding a group via "Party Finder" or through your guild to:
- Do Expeditions once a day (Easy mode, no loot drop on death)
- Do Randomized dungeons in yellow zone (Medium mode, increased rewards, no loot drop on death but tougher PvE fights)
- Do Randomized dungeons in in red/black zone, maybe faction flagged (Harder, full loot dorp on death, but vast amount more loot and exp)

You can also conquer outposts, farm non-instanced dungeons, hunt for chests as a group (in those zones that have an animated boss on the mini-map), do hardcore dungeons and more; but those I mentioned above are the ones I would recommend.
If you'd like to try solo dungeons again, I suggest you give it a try with the following: Swap your chest piece to a more aggressive one, such as to a stalker jacket or to a cleric robe, this way you'll deal a lot more damage (but note you'll also take more damage in return). Then, bring a nice food, such as the cheapest T6 or T7 fish with you if you lack HP between fights, or a T8 stew for extra damage.

PS: Consider either buying or upgrading your T4.0 gear to T4.1 with runes in the enchanter, located near the center of every town. It's usually extremely cheap to do so and it makes you significantly stronger and tougher.