For some reason, the quest "I Could Make You Care" doesn't start, even though I've been in more than three trigger locations listed in the Vault. Is there some way I can force it to start, like a console command or something?

I once got "I Could Make You Care" by getting Euclid's C-Finder (talk to the boy chasing the girl with the toy gun, that toy gun is the C-Finder)

I got and reloaded it already, nothing happens.

Have you completed the Brotherhood of Steel sidequest "Still In The Dark" by any chance? Or do you go to speak to the Elder only to find he says something like "I'm sorry outsider, but I am busy making preparations for the lockdown" and refuses to talk any further?

This might seem unrelated, but I found a connection between the two. I too could not start "I Could Make You Care" - no matter what I'd do, Veronica's trigger dialogue would never happen. I decided to fix both this and my stuck Brotherhood quest using console commands. First up was the Brotherhood problem - and in the process of fixing it, Veronica got fixed as well! Let me explain.

I could not complete Still In The Dark and was getting that blow-off from the Elder. So, following advice in another thread here, I fixed the problem by going into the console and resetting that quest. This is the ONLY console command I needed to issue:

resetquest 0015D79D

That let me start Still In The Dark again, and finish it within a couple of minutes since going and retrieving items again wasn't necessary - just had to do the dialogue paths with the Elder and Lorenzo. Lockdown lifted, I headed back to the Lucky 38 to drop off Boone and pick up Veronica, ready for some console-command forcing of her trigger dialogues. Now, ages and ages ago I noted she wanted a nice dress, so I gave her formal wear. No response. Checked the Wiki and found that she SHOULD have been pleased and given me an unarmed combat perk. She never did. When I asked her to follow me this time, though, as soon as she agreed and I said "goodbye" and left dialogue mode, she whipped straight back into it, saying "oooh thank you! It's so pretty" etc etc etc, and gave me the perk. Hmm, I thought, something's been connecting the SitD quest problem with Veronica and/or vice-versa. I guess she IS a member of the Brotherhood

Went to Vault 3 to trigger her dialogue. Nothing. Went to McCarran. Nothing. Went to Boomers MUseum, which I hadn't been to yet. Took the tour - and got her trigger dialogue. Went to Cottonwood Cove. Nothing. Just about to head for a console reference to force-start the quest, I thought I should try talking to her - it's something the Wiki advised if she didn't talk on her own. As it turned out I had a new dialogue option for her. Used it, talked about the Brotherhood, that was that. Goodbye. And then she asked to talk to ME. Bingo. "I Could Make You Care" was started

So there's definitely some link between at least one unfinished Brotherhood quest and Veronica. This fixed everything for me.

Oh, and important: if you use the above console command to reset Still in the Dark, after doing so, save, quit the game completely and reload it. Otherwise you will no longer get any Steam Achievements for that game session.