Chesapeake Data Systems Corp., which lost a bitter legal battle with Columbia Data Products Inc. this summer in its bid to compete for Columbia's distribution network, yesterday announced that it had begun shipments of its line of IBM-compatible personal computers and peripherals.

The company also announced that it would sell a multi-user computer system compatible with IBM's AT personal computer sometime in November.

Chesapeake, initially incorporated in June, was launched by former Columbia president Robert Cross in the wake of Columbia's Chapter 11 bankruptcy filing in May.

Cross, who had come to Columbia as a "turnaround" executive last year to help reposition the ailing Columbia-based manufacturer of IBM-compatible personal computers, had been unable to work out a satisfactory relationship with the company's bank creditors -- notably National Bank of Washington and First National Bank of Pennsylvania Corp., according to sources close to both Cross and the banks.

However, when Cross and several other former key Columbia executives left to create Chesapeake in June, Columbia's bankruptcy trustee sued in an attempt to block the formation of the new company. The trustee charged that Chesapeake's officers would expropriate Columbia's proprietary technology and its customer lists. The Federal District Court in Rockville issued a temporary restraining order against Chesapeake.

After nearly four weeks of hearings, the court granted Columbia's trustee an injunction that prohibited Chesapeake from contacting 500 of Columbia's top distributors around the world. However, the court did permit Chesapeake to complete an arrangement with Trigem, a Korean computer equipment manufacturer. Chesapeake's new computers are modified versions of Trigem products.

"The injunction has been a difficulty, but we are still attempting to proceed with an appeal," said Cross, who projects Chesapeake will break even by the end of the year and have revenue of more than $20 million in 1986.

"We're alive and well; manufacturing and selling product," said James P. Koch, Columbia's attorney. "We have absolutely no comment whatsoever in respect to Chesapeake."