Is there any reason to believe the CPU isn't soldered on to the motherboard? I haven't seen a laptop with a socket in as long as I can remember....
With no disrespect intended, I do not think you have had one open in a long time then.
Aside from netbooks and ULV-processor notebooks, the vast majority of notebooks use a socketed processor. If they did not, you would need a mainboard production line for every different configuration. It would greatly complicate production and increase costs, as well as increase repair costs. I have upgraded probably a hundred laptop processors over the past 3-4 years.
Socket M - First generation Core Duo, first generation Core 2 Duo
Socket P - Second and third generation Core 2 Duo
The Inspiron 1545 uses Socket P. What processors are supported depends mostly on the chipset.
Intel 945 - Core 2 Duo Merom (most, if not all 945 chipset laptops are Socket M)
Intel 965 - Core 2 Duo Merom, first generation Core 2 Duo Penryn (800MHz FSB only)
Intel 4-series chipset - Core 2 Duo Merom, first and second generation Core 2 Duo Penryn (up to 1066MHz FSB)
Intel also made budget chipsets, the 940GML and 943GML. These are severely limited; the 940GML is limited mostly to Celeron-M and Core Solo chipsets, while the 943GML will support some Core 2 processors, though laptops with these chipsets often use single-core processors for the stock configuration.
The Inspiron 1545 uses a GM45 (a 4-series) chipset, and the T4200 processor is a Penryn-3M core, 800MHz FSB. I would recommend going to a Core 2 P8600 processor, which is still a good deal faster than the T4200, less, expensive than the T9600, and less power-hungry. Anything higher-end will cost so much more that you might as well put the money towards a new laptop and sell this one.
P.S. A 2GB memory module isn't too expensive. Now might be the time to go to 4GB.