Okay, your conundrum for the day. If your new client won't let you do the best work you can for them, is it your fault for trying to push them into something you know is better, or should you just give them what they asked for and take the cash?
One of the realities of doing any kind of design work is that if you land a client who has very bad marketing materials, or worse, truly bizarre materials, and you provide them with the clean branding experience that you know works and will be successful in the marketplace, I will bet you dollars to donuts that they will hate what you have presented them. We've all experienced this. A client will come to you and acknowledge that their present website does not work. In reality, it hasn't worked for five years. Google can't find them, yet by the time you're finished you've ended up with the same website they wanted to get rid of. Crazy.
It happens all the time. If it's not new people making the decisions, but the same folks that approved the crazy-ass website five years ago then they will suddenly not change into Bauhaus aficionados. Your beautiful, clean design will be conservative based on their design aesthetic. They will hate it.
Don't forget someone (most likely the person you're talking to right now) approved that hideous old website. It made people's retinas burn the moment it went live, but someone liked it. And they left it up for years. Perhaps they thought it would get better with age? The sales people liked it. NEVER ASK SALES PEOPLE THEIR OPINION ABOUT ANYTHING TO DO WITH DESIGN.
Part of the problem is that what you're showing them is different. People hate change. And on some level, your sophisticated design is a repudiation of what they did before. Even though they know it has to be fixed, they are really hoping that it doesn't have to be fixed THAT much because, well, you're telling them that they have no taste and their baby was ugly. There is sometimes no winning these situations.
Many years ago in a previous incarnation I did digital slide presentations. There was this one client who frustrated me so badly with his horrendous requests, so much so, that I just tossed out all the designs that I thought would work and showed him a starscape, with a green 3D grid disappearing off into the edge of the universe. Thus Spake Zarathustra was pumping out of the attached speakers. It was the worst, most cliche thing I could think of and the client almost burst into applause, he was so happy. That was what he wanted. He wanted something he saw other people do that he thought was cool.
I'm not suggesting that you should bury your principles. We should always be giving our clients choices that fit the budget. But I'm telling you, if someone has been sitting on a pile of crap for years that's a good indicator of how seriously they are going to take your educated design suggestions. Just don't tell them their kid is ugly.