There is no money.  His parents were only together for a few years before they died.  They were both working and saving money but they already bought a house (which costs a lot of money), and were still having to pay for food and other bills like a family would normally have to do.  Also, babies are expensive!  We emptied our savings when our kid was born, and that wasn't even paying for medical bills, just for diapers and formula and clothing and a crib, and on and on and on.  Even later on when our kid was older and we were both working full time it was very hard to save any money at all.  It's amazing that Harry's parents were able to save enough to put in the vault to get him through his school years as the book had it. 

If Harry hadn't gone to Gemini he would have had plenty of money to get him through his last two years at school and maybe start him off with a flat afterwards, but that isn't the way it is in this story.  He NEEDED to be flat broke in this story to have half of the elements of this story work and to have half of the conflict this story has.  The story would be completely unorignal and boring and flat if he had enough money to just skate through life.  In some stories it makes sense for him to have no money troubles, but in this story those troubles play a prominent role.  I have another story where Harry is filthy rich, but this can't be the case here.

Also, just becuase a family is an old and well known wizarding family doesn't mean they have money.  Take the Blacks for instance.  At some point they may have had money enough to buy that grand house and house elves, but sometimes families squander their inherited money or just keep using it without ever replenishing it (I know a guy who has inherited around $60,000 in the last couple years and within a couple months he had it all spent with nothing to show for it).  Sirius didn't work to replenish the money, and his brother didn't either since he died.  I bet his mom didn't work at all and I could see his father sitting back and relaxing and living off the family money for his entire adult life.  At some point the old family money has to run out if it's not being replenished.  In the books it only ever mentions that Sirius' house was left to Harry and the house elf, but never any money.