Straight wired the cooling fan relay and now car won't start 1995 Chevrolet lumina

SOURCE: Cool fan won't run on

Need to know some specifics for a specifis answer.
To answer in general, Sounds as if you replaced the correct computer temp sensor (it would have a voltage reference signal) and not the gauge sender. The temp may need to reach 235 degrees or so to kick the fan on. Too me that is way too high. But running at a higher temp normally lowers emissions and I think that is the reason for the high temp to kick on a fan.

With a scanner you can see what the temp sensor is reading and when there is a fan request from the computer. Not everyone keeps a scanner for home use.
Do you have A/C and does the fan ever kick on when the A/C is on?

You can try this,
Go to your factory fan relay and figure which is the ground signal wire (the ECM sends a ground signal to trigger the relay. Early wire such as in my 89 IROC is a green with white stripe). Ground this wire with the key on. Does the fan come on?

If the fan comes on, look at the cylinder heads between the exhaust ports. The right side may have a pipe plug towards the rear. Left side it would be up front.
If there is a pipe plug then there is a provision to add a low temp fan switch. Search SummitRacing.com (or another source) for a low temp fan switch. Hypertech makes some. Install that into the port where the pipe plug is (careful of thread sealant as it can interfere with a good ground it needs). Connect the wire from the low temp switch to the ground wire of the relay. You can use a center tap as all you're doing is adding a ground (thats not like something that will draw current which you don't want to do).
This way you have a low temp switch to send a ground signal to the relay and still have the factory computer circuit.

You can get free wire diagrams from autozone.com in the repair section. This way you can look up your specifuc vehicle and see what wires do what and which would be the ground from the ECM.