Hay, a week is really long para sa ganyang edad, lalo na may vomiting pa initially, I'd really suggest you take your 4-year-old to the doctor soon para ma-check properly kung ano talaga ang cause, kasi ang combination ng constipation, stomach pain, at lethargy can be tricky to figure out without checking. A few of my mum friends' kids had similar complaints din, pero turned out iba-iba ang culprit, one was a blockage, isa naman just needed dietary adjustment, so kailangan talaga ng proper exam at assessment. In the meantime, focus siya sa fluids and soft foods, pero please don't delay the doctor visit, ha. Your baby's getting weaker pa, which worries me for you as well.