1987 Toyota Cressida 87 cressida

i just bought my daughter a 1987 toyota Cressida.It had been sitting for a year or more when we got it but only has 110,000 miles and looks good.The seller filled up the tank but said their may be some bad gas in it.I put some SeaFoam in the tank and its been starting up but runs rough for a few minutes then clears out.My daughter got the money to register it and started to use it daily.I told her NOT to let the gas get to low or it may cause it to run rough.well she ran it low but then filled it up with fresh fuel.I drove it the other day and it ran like new!!She took it to work the other night and said it stalled but then started it back up.Well now its sitting in a really unsafe area in Orlando and just turns over but not starting?Her friend who is not a mechanic said he asked someone and they told him the fuel pump may have gone bad?Also he said something about the fuel relay?Like I said he is not close to being a Mechanic but just asked someone he knew.I am going to have it towed to our home.She says its a junker but it is really in great shape for 22 yearrs.My main question is what are the things you would check first before buying a expensive fuel pump?She said it stalled a few times and started back up and she just kept driving.But then it stalled and i asked if any noises or warning and she said no.Now it just turns over and won't crank.Like i mentioned it has been sitting due to the owners relative having cancer but i started it up daily.Thanks for your time and Help as I am glad there is a forum to ask these questions too!!!!!I get disability and its the end of the month but if i get a reply will promise to donate!!
Dave in Fla