If you replaced the solenoid it should not be an issue, but then again new things do go bad, also it might sound silly but check and see if your motor is tight when it is cold, try the solenoid and see what happens, if it is not the new starter might be bad, I have had a bunch of new and reman starters come back to the store. I have one customer who went through two reman starters before he got one that worked.
"Its a Ford. Nuff said. Everything else is just a glorified tonka toy"
"ASE" Certified" Parts Professional
92 F150 302 4x4 Long bed Extended cab
2001 Taurus wagon